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Normal Smarandache Concatenated Numbers
Prime factors from 1 up to n (n=2,3,...,200)
rood Reversed Smarandache Concatenated Numbers rood
rood Repunits Factorization


Itinerary

sm1sm2sm3sm4sm5sm6sm7sm8sm9sm10sm11sm12sm13sm14sm15sm16sm17sm18sm19sm20
sm21sm22sm23sm24sm25sm26sm27sm28sm29sm30sm31sm32sm33sm34sm35sm36sm37sm38sm39sm40
sm41sm42sm43sm44sm45sm46sm47sm48sm49sm50sm51sm52sm53sm54sm55sm56sm57sm58sm59sm60
sm61sm62sm63sm64sm65sm66sm67sm68sm69sm70sm71sm72sm73sm74sm75sm76sm77sm78sm79sm80
sm81sm82sm83sm84sm85sm86sm87sm88sm89sm90sm91sm92sm93sm94sm95sm96sm97sm98sm99sm100
sm101sm102sm103sm104sm105sm106sm107sm108sm109sm110sm111sm112sm113sm114sm115sm116sm117sm118sm119sm120
sm121sm122sm123sm124sm125sm126sm127sm128sm129sm130sm131sm132sm133sm134sm135sm136sm137sm138sm139sm140
sm141sm142sm143sm144sm145sm146sm147sm148sm149sm150sm151sm152sm153sm154sm155sm156sm157sm158sm159sm160
sm161sm162sm163sm164sm165sm166sm167sm168sm169sm170sm171sm172sm173sm174sm175sm176sm177sm178sm179sm180
sm181sm182sm183sm184sm185sm186sm187sm188sm189sm190sm191sm192sm193sm194sm195sm196sm197sm198sm199sm200
Please doublecheck the correctness of the above results before using them for continuing the search!

Legend
sm_Ncompletely factorized
sm_Nsmallest Sm with unknown factors
sm_NSm with unknown factors
sm_NSm is prime (smallest one > Sm344869 ref. E. Weisstein)!


Prefatory Notes & Sources

In the table below you'll find all the prime factors of the concatenation
of numbers from 1 up to n.
These numbers are called  Smarandache Concatenated Numbers. 

The first one with an unknown prime factor is when n = 124.
If there is a breaktrough in partially or completely factorising Sm124, please let me know,
so that I can update the list.

For the factorizations I initially followed the sources from

Micha Fleuren, Smarandache factors
Hans Havermann, Factorization of Smarandache Concatenated Numbers, Sm-n (n < 84)

Other subject related sources on the web

Smarandache Numbers by Dr. M. L. Perez
Smarandache factors by Micha Fleuren
Primes by Listing by Carlos Rivera
Consecutive Number Sequences by Eric W. Weisstein
Smarandache Sequences by Eric W. Weisstein
Smarandache Prime by Eric W. Weisstein
List of factors of the Reversed Smarandache Concatenated Numbers by Patrick De Geest

Book sources

“Some Notions and Questions in Number Theory”, by C.Dumitrescu and V.Seleacu, Glendale, AZ:Erhus University Press, 1994.
(communicated to me by Marin Petrescu (email) from Bucharest)
“CRC Concise Encyclopedia of Mathematics”, by Eric W. Weisstein, CRC Press, Boca Raton, Florida, 1998.
(communicated to me by M.L. Perez (email))

OEIS entries (some sequences for illustration purpose)

A007908 - Concatenation of the numbers from 1 to n.
A019519 - Concatenate odd numbers.
A046460 - Number of prime factors of concatenation of numbers from 1 up to n, with multiplicity.
A046461 - Numbers n such that concatenation of numbers from 1 to n is a semiprime.
A046462 - Concatenation of numbers from 1 to a(n) has exactly 3 prime factors, with multiplicity.
A046463 - Concatenation of numbers from 1 to a(n) has exactly 4 prime factors, with multiplicity.
A046464 - Concatenation of numbers from 1 to a(n) has exactly 5 prime factors, with multiplicity.
A046465 - Concatenation of numbers from 1 to a(n) has exactly 6 prime factors, with multiplicity.
A046466 - Concatenation of numbers from 1 to a(n) has exactly 7 prime factors, with multiplicity.
A046467 - Concatenation of numbers from 1 to a(n) has exactly 8 prime factors, with multiplicity.
A046468 - Concatenation of numbers from 1 to a(n) has exactly 9 prime factors, with multiplicity.
A048342 - Numbers n such that the concatenation of the numbers 1, 2, ..., n is a product of distinct primes.
A050675 - Numbers n such that concatenation of numbers from 1 to n is nonsquarefree.
A050676 - Let b(n) = number of prime factors (with multiplicity) of concatenation of numbers from 1 to n; sequence gives smallest number m with b(m) = n.
A053067 - (n) is the concatenation of next n numbers (omit leading 0's).
A066811 - Numbers k such that the concatenation of odd numbers from 1 to k is a prime.
A089987 - Primes in the concatenation of consecutive numbers beginning with 2.
A105311 - a(n) = n concatenations of numbers from 1 to n, concatenated.
A241569 - Primes of the form: (concatenation of first n positive integers) + 1.
A241570 - Primes of the form: (concatenation of first n positive integers) – 1.
A259937 - Concatenation of the numbers from 1 to n with numbers from n down to 1.
A262299 - Let S(n) denote the sequence formed by concatenating the decimal numbers 1,2,3,..., omitting n; a(n) is the smallest prime in S(n), or -1 if no term in S(n) is prime.
A262300 - Let S(n,k) denote the number formed by concatenating the decimal numbers 1,2,3,...,k, but omitting n; a(n) is the smallest k for which S(n,k) is prime, or -1 if no term in S(n,*) is prime.
A262571 - Concatenation of the numbers from 2 to n.
A262577 - Concatenation of the numbers from 1 to n but omitting 7.
A279610 - a(n) = concatenate n consecutive integers, starting with the last number of the previous batch.

PrimeForm or PFGW

To calculate the length of a Smarandache number in PrimeForm you just enter at the prompt
pfgw64 -od -f0 -q"len(Sm(119))"
For the reversed Smarandache number you type
pfgw64 -od -f0 -q"len(Smr(119))"


Some Factorization Websites

Factorization using the Elliptic Curve Method
GGNFS - A Number Field Sieve implementation


Messages

[ April 25, 2015 ]
Stephen Tucker's (email) search for prime Smarandache numbers !

Dear Patrick,
I have found your list of Smaradache factors and noticed that no prime Smarandache number
has been found yet. Well, I decided to try looking for one.
Using Dario Alpern's ECM Factorizing applet, (and software I wrote myself to generate the numbers),
I have discovered that there are no prime Smarandache numbers less than Sm2659.
When I tried using Dario's applet to factorize Sm2659 (which, by the way, has no factors less than
or equal to 39989) the applet's attempt to start the Prime Check routine stalled.
I tried using it to check Sm2713, but the same thing happened again.
Dario's website does stipulate a maximum length of input number of 10000 digits. However, Sm2659
is "only" 9529 digits long, so perhaps his stated limit of 10000 is rounded up.
After a brief search on the web, I haven't discovered anything about prime Smaradanche numbers.
I wonder if it could be that a Smaradanche number cannot be prime.

Hope this is of interest.

Yours,
Stephen Tucker (UK).

Answer

Eric Weisstein [ http://mathworld.wolfram.com/ConsecutiveNumberSequences.html ]
wrote he extended the search up to 38712 terms which is
quite ahead of your Sm2659. He did find a probable prime for
the reversed case though (Rsm37765).

Note Primeform with the program PFGW64.EXE has a built-in command
Sm(x) and Smr(x) to search for (probable) primes directly.
I did a run up to Sm(10000) and found indeed none. For larger
values one needs a faster computer than I have at the moment.
So there is still opportunity to detect the first PRP Sm !

[ May 20, 2008 ]
Greg Childers (email) factorized Sm99 ! [ go to entry ]

Hi Patrick,

I finally got around to factoring Sm99 by SNFS. As for Sm94, I used
the GGNFS lattice siever and msieve for the postprocessing. The factors are

P65: 37726668883887938032416757819314355053940153680075342644295667759

P107: 14627910783072606795565990651314126145674770336615677946549896262532933945988541999815567058347827465728809

Greg

[ December 9, 2007 ]
Greg Childers (email) factorized Sm94 ! [ go to entry ]

Hi Patrick,

Here are the factors of Sm94. This was completed using SNFS.
GGNFS was used for the sieving and msieve for the post-processing.

p79: 1825097233762709447432521941926649289213154260264910537140594516431173070300371

p82: 2674525573684858697560701870658348933916102325593721165422426453989766526938215889

Greg

[ June 8, 2006 ]
Sean A. Irvine (email)

Excellent work! (reg. Sm98 by Ph. Strohl)

Sm94 is still struggling. My yield has dropped below 1 and I've sieved
to special-q 70M already, but still don't have enough relations.

S.

[ June 6, 2006 ]
Philippe Strohl (email)

Hi Patrick !
I have factorized the remaining part of the 98th Smarandache
concatenated number. It was a 126 digits composite.
I have obtained it with ggnfs (a wonderful program : I have done it with
a common laptop computer with "only" 512 megs of ram and a 1.4 GHz
celeron M in two weeks).

the results :
N = 709891330215674922888729762564179876071621230485156504316706784486089628388958197669654729613064737223993515869067455247541707
( 126 digits)
Divisors found:
r1=3588472635471667861938967869443938442910813342994227048889 (pp58)
r2=197825482406769698151783117995020967519766027202915861687264259155363 (pp69)
Version: GGNFS-0.77.1-20060513-pentium-m
(prp verified prime with apr-cl)

Thanks for your site and for keeping tracks of our work.
Best regards.

Philippe Strohl

[ September 11, 2005 ]
Sean A. Irvine (email)

The next two have finished:

Sm87 C145 =
(p51) * (p95)
by SNFS, 14 days

Sm88 C153 =
(p42) * (p51) * (p61)
by GNFS, 8 hours

Sm90 looks like it will have to be SNFS since ECM has failed
to find a factor.

Regards,
Sean.

[ August 29, 2005 ]
Philippe Strohl (email)

Hi Patrick !
Thanks for accepting my "colouring" idea ! I am very pleased !

I should report you this 39 digits factor for Sm98 (Partial factorization):

Sm98* 2.3^2.23.37.199
p16: 1495444452918817(MF)
c165: 270825497607069872452415496119443135107702791840293286471110488510
4768274391266695197120574357173627794391936143016235446328574795690351940341420
23605896434694145167

Line=16/32 Curves=47/1000 B1=1000000 factors=0
C165 Using B1=1000000, B2=839549780, polynomial Dickson(6), sigma=594918519
Step 1 took 28422ms
Step 2 took 18926ms
********** Factor found in step 2: 381502754125464943168932369122248696781
Found probable prime factor of 39 digits:
381502754125464943168932369122248696781

Composite cofactor
709891330215674922888729762564179876071621230485156504316706784486089628388958197669654729613064737223993515869067455247541707
has 126 digits

Thanks again.

Best regards.
Philippe Strohl

[ August 29, 2005 ]
Sean A. Irvine (email)

Here is the last part of Sm86:

10828687641092318839822035841363590407263202742239027773 (p56) *
1089075252400674157091531724111232381528208779232955680665273 (p61)
by GNFS, 2 days.

As before I'm now working on Sm87.

Sean.

[ August 28, 2005 ]
Sean A. Irvine (email) latest results.

Here are my latest results. Like I mentioned earlier
I expect to complete Sm86 today as well:

Sm83 C134
21875480270521598141087357354188092945840550359281483 (p53) *
3966169790267211790412249283896602109358687165012835285295541472324348526743126307 (p82)
by SNFS, 8 days

Sm85 C158 =
120549814855596987772827562271063563633851059 (p45) *
Using B1=11000000, sigma=1708124291
2112809210944968177871685727287164545437750155430310661 (p55) *
197843626412162026434764405036310959588059884460495810550047 (p60)
by GNFS, 1 day

Sm86 C154 =
718252229986396496762902999331863301257 (p39) * C116
Using B1=11000000, sigma=3414478964
C116 by GNFS nearly done

Sm87 C145 Sieving by SNFS started 2005-08-29.

Others with B1=1e6 (I have now completed 1000 curves with B1=1e6
on all Sm(n), n ⩽ 200)

Sm114 8678622406220213516465050301044327
Sm159 45941358846148651407783221723920871719
Sm171 40202471819457246557501649563881337
Sm193 5167315927941164272437909427556797

Sean.
It seems that a fierce competition is going on. But to avoid
duplicate work and loose valuable cpu time I advice strongly
to make arrangements among yourselves!

[ August 28, 2005 ]
Philippe Strohl (email)

..., for example : the smallest unfactored Sm number is sm83
(unfactored) but I have factored last year Sm85 (involving a p45 found by
ecm) and Sm86 (with a p39 and a ggnfs on the remaining c115)... This
represents quite a large amount of cpu work. Sm84 factorization is still
known on M Fleuren page...

[ August 3, 2005 ]
Sean A. Irvine (email) completely factorized Sm78 ! [ go to entry ]

Sm78 C139 =
205155431830422787082756234197593935249202704547671264423 (p57) *
17403902113720391120287411398887911225298966708915583006414519403038472992542973083 (p83)
by GNFS (General Number Field Sieve), 9 days

Here is a bunch more factors for higher values which I have not seen
previously reported. All these were found with ECM B1=1e6.

Sm89 496118159817126721484175235476073
Sm89 26459905787227421825352754831024262009257.P64
Sm92 46731404628893905607210235741707
Sm93 19544056951015647623992763251
Sm95 244987542265129586458446183157595351.P141
Sm100 970447246795177523033247400823.P118
Sm106 95383501607400293616004374931
Sm106 54259599094002572583355411045946413
Sm108 132761751746390611923240080737166083.P161
Sm109 9943216978062352390003139833531
Sm114 2042059881000388200555074336219
Sm116 9787002048140152171263515060558503699.P198
Sm121 105299178204417486675841093021769.P214
Sm123 12347002211187670552593982429
Sm123 2829927788416784955921382453753
Sm125 295999706346724665505289
Sm137 144065103514544138702103468451
Sm148 8817212782626223819399721069204897.P254
Sm152 4103096315830350734534473515557
Sm152 12805089500421274253268517941967
Sm152 17815076027044127272632744936161.P205
Sm154 32063206397901252963254536935569
Sm159 11855111297257593607972759339201
Sm160 64603936118676024484144135734907
Sm162 22260247937572504750086047
Sm164 1039418554780603268384723777072953
Sm165 13183356310254866666237435750357.P328
Sm176 1011379313630785579015894871
Sm183 553245689211853052761209813199
Sm184 677008100402429325901609057.P342
Sm187 1080829169904060835770214147747.P411
Sm193 419908232491384495189
Sm195 165897663095213559529993681.P412
Sm198 14158849264684185910199571953

Further, after studying Backstrom's work on Rsm76 I am now able to generate
SNFS polynomials for all the remaining Sm numbers below 100. It would have
been much faster to do Sm78 by SNFS, but I had already started it before
working out how to apply SNFS to the number. It should be possible to complete
all values up to Sm(100) by SNFS, although a few will be quite difficult runs.

The next smallest unfactored number of this form is now Sm83[C134].

Sean.

[ November 18, 2004 ]
Sean A. Irvine (email) completely factorized Sm75 ! [ go to entry ]

It took him 13 days, by using GNFS.
Well done, congratulations for factoring Sm75(c133) into this p47 * p87 :
38824496309870038690197243565592769246963314017 (p47) *
219358378032318168161320006998916878634145966511629131235131312083699783021949850982403 (p87)

Next challenge is this composite factor of 139 digits of Sm78 :
3570505053674714753162296261527331568459971771942/
9181309659088118527251315326728064046015264067596/
03889145976969679985423963150530264526109

[ March 23, 2004 ]
Philippe Strohl (email) completely factorized Sm73 ! [ go to entry ]

Hello Patrick !

This mail to inform you that the factorization of the 73th concatenated smarandache number is now complete
with the discovery of a p46 by GMP-ECM...

Sm73 = 37907.p46.p87
p46: 1612352371081094864112011094480307952600705089
p87: 201992666185187831800817490810938117880341395186600971262233773863756955874363353778851
...
Sm74 factorization is known and the next composite to challenge is Sm75
with no factors expected below 35 digits...

Sm74 = 2.3.7.1788313.21565573.p20.p25.p31.p49
p20: 99014155049267797799
p25: 1634187291640507800518363(PZ)
p31: 1981231397449722872290863561307
p49: 2377534541508613492655260491688014802698908815817

Sm75* 3.5^2.193283.c133
c133:
851647853845481367839983983361331811035304896846801931077529055832/
3936344974946612980172082837107906069172212808249295700548030242851


The List of Sm Factors






 1


Sm1 = p1  [ Length = 1 ] unity 



1







 12


Sm2 = (p1)^2 * p1 [ Length = 2 ]



2^2 * 
3







 123


Sm3 = p1 * p2  [ Length = 3 ] semiprime 



3 * 
41







 1234


Sm4 = p1 * p3  [ Length = 4 ] semiprime 



2 * 
617







 12345


Sm5 = p1 * p1 * p3 [ Length = 5 ]



3 * 
5 * 
823







 123456


Sm6 = (p1)^6 * p1 * p3 [ Length = 6 ]



2^6 * 
3 * 
643







 1234567


Sm7 = p3 * p4  [ Length = 7 ] semiprime 



127 * 
9721







 12345678


Sm8 = p1 * (p1)^2 * p2 * p5 [ Length = 8 ]



2 * 
3^2 * 
47 * 
14593







 123456789


Sm9 = (p1)^2 * p4 * p4 [ Length = 9 ]



3^2 * 
3607 * 
3803







 12345678910


Sm10 = p1 * p1 * p10 [ Length = 11 ]



2 * 
5 * 
1234567891







 1234567891011


Sm11 = p1 * p1 * p2 * p2 * p3 * p6 [ Length = 13 ]



3 * 
7 * 
13 * 
67 * 
107 * 
630803







 1234567...12


Sm12 = (p1)^3 * p1 * p4 * p10 [ Length = 15 ]



2^3 * 
3 * 
2437 * 
2110805449







 1234567...13


Sm13 = p3 * p6 * p9 [ Length = 17 ]



113 * 
125693 * 
869211457







 1234567...14


Sm14 = p1 * p1 * p18 [ Length = 19 ]



2 * 
3 * 
205761315168520219







 1234567...15


Sm15 = p1 * p1 * p19 [ Length = 21 ]



3 * 
5 * 
8230452606740808761







 1234567...16


Sm16 = (p1)^2 * p10 * p13 [ Length = 23 ]



2^2 * 
2507191691 * 
1231026625769







 1234567...17


Sm17 = (p1)^2 * p2 * p4 * p18 [ Length = 25 ]



3^2 * 
47 * 
4993 * 
584538396786764503







 1234567...18


Sm18 = p1 * (p1)^2 * p2 * p5 * p18 [ Length = 27 ]



2 * 
3^2 * 
97 * 
88241 * 
801309546900123763







 1234567...19


Sm19 = p2 * p2 * p2 * p3 * p4 * p18 [ Length = 29 ]



13 * 
43 * 
79 * 
281 * 
1193 * 
833929457045867563







 1234567...20


Sm20 = (p1)^5 * p1 * p1 * p6 * p7 * p16 [ Length = 31 ]



2^5 * 
3 * 
5 * 
323339 * 
3347983 * 
2375923237887317







 1234567...21


Sm21 = p1 * p2 * p2 * p2 * p3 * p3 * p6 * p18 [ Length = 33 ]



3 * 
17 * 
37 * 
43 * 
103 * 
131 * 
140453 * 
802851238177109689







 1234567...22


Sm22 = p1 * p1 * p4 * p4 * p5 * p22 [ Length = 35 ]



2 * 
7 * 
1427 * 
3169 * 
85829 * 
2271991367799686681549







 1234567...23


Sm23 = p1 * p2 * p3 * p32 [ Length = 37 ]



3 * 
41 * 
769 * 
13052194181136110820214375991629







 1234567...24


Sm24 = (p1)^2 * p1 * p1 * p18 * p19 [ Length = 39 ]



2^2 * 
3 * 
7 * 
978770977394515241 * 
1501601205715706321







 1234567...25


Sm25 = (p1)^2 * p5 * p11 * p25 [ Length = 41 ]



5^2 * 
15461 * 
31309647077 * 
1020138683879280489689401







 1234567...26


Sm26 = p1 * (p1)^4 * p5 * p7 * p12 * p18 [ Length = 43 ]



2 * 
3^4 * 
21347 * 
2345807 * 
982658598563 * 
154870313069150249







 1234567...27


Sm27 = (p1)^3 * (p2)^2 * p4 * p5 * p32 [ Length = 45 ]



3^3 * 
19^2 * 
4547 * 
68891 * 
40434918154163992944412000742833







 1234567...28


Sm28 = (p1)^3 * p2 * p3 * p15 * p27 [ Length = 47 ]



2^3 * 
47 * 
409 * 
416603295903037 * 
192699737522238137890605091







 1234567...29


Sm29 = p1 * p3 * p20 * p26 [ Length = 49 ]



3 * 
859 * 
24526282862310130729 * 
19532994432886141889218213







 1234567...30


Sm30 = p1 * p1 * p1 * p2 * p8 * p18 * p23 [ Length = 51 ]



2 * 
3 * 
5 * 
13 * 
49269439 * 
370677592383442753 * 
17333107067824345178861







 1234567...31


Sm31 = p2 * p10 * p42 [ Length = 53 ]



29 * 
2597152967 * 
163915283880121143989433769727058554332117







 1234567...32


Sm32 = (p1)^2 * p1 * p1 * p23 * p30 [ Length = 55 ]



2^2 * 
3 * 
7 * 
45068391478912519182079 * 
326109637274901966196516045637







 1234567...33


Sm33 = p1 * p2 * p3 * p4 * p18 * p31 [ Length = 57 ]



3 * 
23 * 
269 * 
7547 * 
116620853190351161 * 
7557237004029029700530634132859







 1234567...34


Sm34 = p1 * p58  [ Length = 59 ] semiprime



2 * 
6172839455055606570758085909601061116212631364146515661667







 1234567...35


Sm35 = (p1)^2 * p1 * p3 * p3 * p8 * p10 * p37 [ Length = 61 ]



3^2 * 
5 * 
139 * 
151 * 
64279903 * 
4462548227 * 
4556722495899317991381926119681186927







 1234567...36


Sm36 = (p1)^4 * (p1)^2 * p3 * p3 * p56 [ Length = 63 ]



2^4 * 
3^2 * 
103 * 
211 * 
39448709943503776711542648338171477043440283875433388943







 1234567...37


Sm37 = p2 * p5 * p7 * p52 [ Length = 65 ]



71 * 
12379 * 
4616929 * 
3042410911077206144807069396988766146557218727107817







 1234567...38


Sm38 = p1 * p1 * p23 * p43 [ Length = 67 ]



2 * 
3 * 
86893956354189878775643 * 
2367958875411463048104007458352976869124861







 1234567...39


Sm39 = p1 * p2 * p3 * p4 * p25 * p36 [ Length = 69 ]



3 * 
67 * 
311 * 
1039 * 
6216157781332031799688469 * 
305788363093026251381516836994235539







 1234567...40


Sm40 = (p1)^2 * p1 * p4 * p5 * p6 * p10 * p20 * p26 [ Length = 71 ]



2^2 * 
5 * 
3169 * 
60757 * 
579779 * 
4362289433 * 
79501124416220680469 * 
15944694111943672435829023







 1234567...41


Sm41 = p1 * p3 * p6 * p8 * p56 [ Length = 73 ]



3 * 
487 * 
493127 * 
32002651 * 
53545135784961981058419604998638516483529257158438201753







 1234567...42


Sm42 = p1 * p1 * p3 * p3 * p11 * p25 * p34 [ Length = 75 ]



2 * 
3 * 
127 * 
421 * 
22555732187 * 
4562371492227327125110177 * 
3739644646350764691998599898592229







 1234567...43


Sm43 = p1 * p2 * p3 * p72 [ Length = 77 ]



7 * 
17 * 
449 * 
231058353953907153927797941629430896528705484237484443924582239474910453







 1234567...44


Sm44 = (p1)^3 * (p1)^2 * p26 * p52 [ Length = 79 ]



2^3 * 
3^2 * 
12797571009458074720816277 * 
1339846151380678925030581935625950075102697197563351







 1234567...45


Sm45 = (p1)^2 * p1 * p1 * p2 * p3 * p4 * p13 * p18 * p41 [ Length = 81 ]



3^2 * 
5 * 
7 * 
41 * 
727 * 
1291 * 
2634831682519 * 
379655178169650473 * 
10181639342830457495311038751840866580037







 1234567...46


Sm46 = p1 * p2 * p3 * p9 * p18 * p25 * p28 [ Length = 83 ]



2 * 
31 * 
103 * 
270408101 * 
374332796208406291 * 
3890951821355123413169209 * 
4908543378923330485082351119







 1234567...47


Sm47 = p1 * p4 * p6 * p22 * p53 [ Length = 85 ]



3 * 
4813 * 
679751 * 
4626659581180187993501 * 
27186948196033729596487563460186407241534572026740723







 1234567...48


Sm48 = (p1)^2 * p1 * p3 * p4 * p7 * p29 * p46 [ Length = 87 ]



2^2 * 
3 * 
179 * 
1493 * 
1894439 * 
15771940624188426710323588657 * 
1288413105003100659990273192963354903752853409







 1234567...49


Sm49 = p2 * p3 * p7 * p10 * p23 * p47 [ Length = 89 ]



23 * 
109 * 
3251653 * 
2191196713 * 
53481597817014258108937 * 
12923219128084505550382930974691083231834648599







 1234567...50


Sm50 = p1 * p1 * (p1)^2 * p2 * p3 * p5 * p18 * p20 * p44 [ Length = 91 ]



2 * 
3 * 
5^2 * 
13 * 
211 * 
20479 * 
160189818494829241 * 
46218039785302111919 * 
19789860528346995527543912534464764790909391







 1234567...51


Sm51 = p1 * p20 * p73 [ Length = 93 ]



3 * 
17708093685609923339 * 
2323923950500978408934946776574079545611397611995364705071565292612305003







 1234567...52


Sm52 = (p1)^7 * p17 * p76 [ Length = 95 ]



2^7 * 
43090793230759613 * 
2238311464092386636761884511894978048448617178182150344531477542781856216843







 1234567...53


Sm53 = (p1)^3 * (p1)^3 * p18 * p76 [ Length = 97 ]



3^3 * 
7^3 * 
127534541853151177 * 
1045271879581348729278017817925065799872257805888381045072615907010178634849







 1234567...54


Sm54 = p1 * (p1)^6 * p2 * p3 * p4 * p5 * p11 * p22 * p51 [ Length = 99 ]



2 * 
3^6 * 
79 * 
389 * 
3167 * 
13309 * 
69526661707 * 
8786705495566261913717 * 
107006417566370797549761092803112128112769421435739







 1234567...55


Sm55 = p1 * p9 * p15 * p22 * p55 [ Length = 101 ]



5 * 
768643901 * 
641559846437453 * 
1187847380143694126117 * 
4215236719202000513320239996510510828557825033460062191







 1234567...56


Sm56 = (p1)^2 * p1 * p25 * p77 [ Length = 103 ]



2^2 * 
3 * 
4324751743617631024407823 * 
23788800764365032854813369830458732886158417401021113465643479155975828316681







 1234567...57


Sm57 = p1 * p2 * p8 * p13 * p37 * p47 [ Length = 105 ]



3 * 
17 * 
36769067 * 
2205251248721 * 
2128126623795388466914401931224151279 * 
14028351843196901173601082244449305344230057319







 1234567...58


Sm58 = p1 * p2 * p31 * p75 [ Length = 107 ]



2 * 
13 * 
1448595612076564044790098185437 * 
327789067063631145720134335581588856152921479945230066396717484857630796759







 1234567...59


Sm59 = p1 * p18 * p36 * p55 [ Length = 109 ]



3 * 
340038104073949513 * 
324621819487091567830636828971096713 * 
3728107520554143574058126525447653708074390492098041537







 1234567...60


Sm60 = (p1)^3 * p1 * p1 * p2 * p3 * p104 [ Length = 111 ]



2^3 * 
3 * 
5 * 
97 * 
157 * 
67555753880267981819314968257940564232852139165917171861439543181780049107204700168947673874146559500327







 1234567...61


Sm61 = p8 * p14 * p92 [ Length = 113 ]



10386763 * 
35280457769357 * 
33689963756771087787406890988794422071942750389483226687410462898596940470571223420915460371







 1234567...62


Sm62 = p1 * (p1)^2 * p4 * p6 * p7 * p34 * p64 [ Length = 115 ]



2 * 
3^2 * 
1709 * 
329167 * 
1830733 * 
9703956232921821226401223348541281 * 
6862941251271421600892952202464376235224342144596167046191804311







 1234567...63


Sm63 = (p1)^2 * p11 * p43 * p63 [ Length = 117 ]



3^2 * 
17028095263 * 
2435984189933032657913735712547671618367909 * 
330698276590517405413770500371046766676563523569978590938716221







 1234567...64


Sm64 = (p1)^2 * p1 * p2 * p2 * p3 * p6 * p19 * p29 * p60 [ Length = 119 ]



2^2 * 
7 * 
17 * 
19 * 
197 * 
522673 * 
1072389445090071307 * 
20203723083803464811983788589 * 
611891180337745942599768541236768900814521123060392220304537







 1234567...65


Sm65 = p1 * p1 * p2 * p5 * p43 * p70 [ Length = 121 ]



3 * 
5 * 
31 * 
83719 * 
8018741962917674781000851595476715337223177 * 
3954865825608609239925917139441010044747553878722812487568124023324127







 1234567...66


Sm66 = p1 * p1 * p1 * p5 * p6 * p36 * p36 * p39 [ Length = 123 ]



2 * 
3 * 
7 * 
20143 * 
971077 * 
319873117219722504963051951872747251 * 
927600480728565729398211282118577179 * 
506464674142683362314480915373647544917







 1234567...67


Sm67 = p3 * p18 * p105 [ Length = 125 ]



397 * 
183783139772372071 * 
169207186381096030569641287629182352063847752831832860300985727686482291228260812667458777140342739211041







 1234567...68


Sm68 = (p1)^4 * p1 * p2 * p9 * p10 * p50 * p56 [ Length = 127 ]



2^4 * 
3 * 
23 * 
764558869 * 
1811890921 * 
16210201583355429120740178111425145802012035286597 * 
49798299077316075944525952275152868666920234906076151289







 1234567...69


Sm69 = p1 * p2 * p2 * p22 * p24 * p32 * p49 [ Length = 129 ]



3 * 
13 * 
23 * 
8684576204660284317187 * 
281259608597535749175083 * 
15490495288652004091050327089107 * 
3637485176043309178386946614318767365372143115591







 1234567...70


Sm70 = p1 * p1 * p7 * p24 * p41 * p60 [ Length = 131 ]



2 * 
5 * 
2411111 * 
109315518091391293936799 * 
11555516101313335177332236222295571524323 * 
405346669169620786437208619979711016226055320437594464205451







 1234567...71


Sm71 = (p1)^2 * p2 * p4 * p31 * p95 [ Length = 133 ]



3^2 * 
83 * 
2281 * 
7484379467407391660418419352839 * 
96808455591058960266687738381050176698103277406505724847082994829643349780363432993640165860627







 1234567...72


Sm72 = (p1)^2 * (p1)^2 * p4 * p27 * p103 [ Length = 135 ]



2^2 * 
3^2 * 
5119 * 
596176870295201674946617769 * 
1123704769960650101739921630151581054522510738566183226239911321871780637830758881774623162921434662407







 1234567...73


Sm73 = p5 * p46 * p87 [ Length = 137 ]  (by Philippe Strohl )



37907 * 
1612352371081094864112011094480307952600705089 * 
201992666185187831800817490810938117880341395186600971262233773863756955874363353778851



Factor p46 Sm73 by GMP-ECM
Sm73 = 37907.p46.p87

None of these factors could have been found by P-1 or P+1 with B1<10^14 and I was lucky
enough to catch the p46 with a ECM B1 of 10^6.

The group order of the curve is very smooth (B1=620227 and B2=1473569 are enough).

325683354264679693500307906698027336176043019186246110832678756888/
805244789707561834881407263896785700945962383243895973215176272739 (132 digits)
Using B1=2000000, B2=5000000, polynomial x^6, sigma=2799427343
Step 1 took 181065ms
********** Factor found in step 1: 1612352371081094864112011094480307952600705089
Found probable prime factor of 46 digits: 1612352371081094864112011094480307952600705089
Probable prime cofactor 201992666185187831800817490810938117880341395186600971262233773863756955874363353778851
has 87 digits (both proven prime by S. Tomabechi APR-CL part of p_1 program)







 1234567...74


Sm74 = p1 * p1 * p1 * p7 * p8 * p20 * p25 * p31 * p49 [ Length = 139 ]



2 * 
3 * 
7 * 
1788313 * 
21565573 * 
99014155049267797799 * 
1634187291640507800518363 * 
1981231397449722872290863561307 * 
2377534541508613492655260491688014802698908815817







 1234567...75


Sm75 = p1 * (p1)^2 * p6 * p47 * p87 [ Length = 141 ]  (by Sean A. Irvine )



3 * 
5^2 * 
193283 * 
38824496309870038690197243565592769246963314017 * 
219358378032318168161320006998916878634145966511629131235131312083699783021949850982403







 1234567...76


Sm76 = (p1)^3 * p18 * p27 * p97 [ Length = 143 ]



2^3 * 
828699354354766183 * 
213643895352490047310058981 * 
8716407028594814374740596028898426313034395366012872513707917231855753694435270081076237925828389







 1234567...77


Sm77 = p1 * p24 * p24 * p39 * p58 [ Length = 145 ]



3 * 
383481022289718079599637 * 
874911832937988998935021 * 
164811751226239402858361187055939797929 * 
7442132227048590901854639419294226672231934035068486536423







 1234567...78


Sm78 = p1 * p1 * p2 * p6 * p57 * p83 [ Length = 147 ]  (by Sean A. Irvine )



2 * 
3 * 
31 * 
185897 * 
205155431830422787082756234197593935249202704547671264423 * 
17403902113720391120287411398887911225298966708915583006414519403038472992542973083







 1234567...79


Sm79 = p2 * p3 * p20 * p24 * p29 * p74 [ Length = 149 ]



73 * 
137 * 
22683534613064519783 * 
132316335833889742191773 * 
35488612864124533038957177977 * 
11589330059060921218833486882285427414280233987959540582909167514265308253







 1234567...80


Sm80 = (p1)^2 * (p1)^3 * p1 * p3 * p8 * p25 * p115 [ Length = 151 ]



2^2 * 
3^3 * 
5 * 
101 * 
10263751 * 
1295331340195453366408489 * 
1702600917839548328745392482587491026230318172323434581398602992701169952537157469971305061091390839579932352102383







 1234567...81


Sm81 = (p1)^3 * p3 * p30 * p119 [ Length = 153 ]



3^3 * 
509 * 
152873624211113444108313548197 * 
58762581888644185603361112342786137599799640821735382180404307223995625796855706598141292123658134092320545833186103011







 1234567...82


Sm82 = p1 * p2 * p4 * p5 * p35 * p42 * p70 [ Length = 155 ]



2 * 
29 * 
4703 * 
10091 * 
12295349967251726424104854676730107 * 
334523571229968373890203385137399026475051 * 
1090461105551993653223776199179348475393504023636425991597284018461539







 1234567...83


Sm83 = p1 * p2 * p3 * p18 * p53 * p82 [ Length = 157 ]  (by Sean A. Irvine )



3 * 
53 * 
503 * 
177918442980303859 * 
21875480270521598141087357354188092945840550359281483 * 
3966169790267211790412249283896602109358687165012835285295541472324348526743126307



by SNFS, 8 days







 1234567...84


Sm84 = (p1)^5 * p1 * p157 [ Length = 159 ]



2^5 * 
3 * 
1286008219803251368907934564500221065877631534197190762847328503894160459817025473591130156786722443288099853756419412985069550726116382682039247695813352379







 1234567...85


Sm85 = p1 * (p1)^2 * p45 * p55 * p60 [ Length = 161 ]  (by Sean A. Irvine )



5 * 
7^2 * 
120549814855596987772827562271063563633851059 * 
2112809210944968177871685727287164545437750155430310661 * 
197843626412162026434764405036310959588059884460495810550047



Sm85 C158 =
120549814855596987772827562271063563633851059 (p45) *
Using B1=11000000, sigma=1708124291
2112809210944968177871685727287164545437750155430310661 (p55) *
197843626412162026434764405036310959588059884460495810550047 (p60)
by GNFS, 1 day







 1234567...86


Sm86 = p1 * p1 * p2 * p7 * p39 * p56 * p61 [ Length = 163 ]  (by Sean A. Irvine )



2 * 
3 * 
23 * 
1056149 * 
718252229986396496762902999331863301257 * 
10828687641092318839822035841363590407263202742239027773 * 
1089075252400674157091531724111232381528208779232955680665273



Sm86 C154 =
718252229986396496762902999331863301257 (p39) * C116
Using B1=11000000, sigma=3414478964
10828687641092318839822035841363590407263202742239027773 (p56) *
1089075252400674157091531724111232381528208779232955680665273 (p61)
by GNFS, 2 days.







 1234567...87


Sm87 = p1 * p1 * p9 * p10 * p51 * p95 [ Length = 165 ]  (by Sean A. Irvine )



3 * 
7 * 
231330259 * 
4275444601 * 
101784611215757903569658774280830604745279416597473 * 
58398250025786270255235847423735930777973447337337804788906368149837276410666257137526766841721



Sm87 C145 = (p51) * (p95)
by SNFS, 14 days.







 1234567...88


Sm88 = (p1)^2 * p14 * p42 * p51 * p61 [ Length = 167 ]  (by Sean A. Irvine )



2^2 * 
12414068351873 * 
462668377429470430246269302055630668010673 * 
144494999796935291164027251780366969508458166480331 * 
3718931833006826909360514481439595803175244655637881136348103



Sm88 C153=
462668377429470430246269302055630668010673 (p42)
B1=11000000, sigma=1512552247
144494999796935291164027251780366969508458166480331 (p51) *
3718931833006826909360514481439595803175244655637881136348103 (p61)
by GNFS, 8 hours







 1234567...89


Sm89 = (p1)^2 * p2 * p2 * p2 * p9 * p18 * p33 * p41 * p64 [ Length = 169 ]  (by Sean A. Irvine )



3^2 * 
13 * 
31 * 
97 * 
163060459 * 
789841356493369879 * 
496118159817126721484175235476073 * 
26459905787227421825352754831024262009257 * 
2075552579046417801880667285191357553672027185826871770761977511







 1234567...90


Sm90 = p1 * (p1)^2 * p1 * p4 * p6 * p7 * p67 * p87 [ Length = 171 ]  (by Sean A. Irvine )



2 * 
3^2 * 
5 * 
1987 * 
179827 * 
2166457 * 
5469640487155071172064105436159054827205011884517193846381587779057 * 
323974513721871489318385733207245357406204798917206286895918649972193592038458818136011



Sm90 C154=
(p67) * (p87)
by SNFS, 32 days

Submitted on Monday October 24, 2005 22:51







 1234567...91


Sm91 = p2 * p3 * p16 * p24 * p55 * p75 [ Length = 173 ]  (by Sean A. Irvine )



37 * 
607 * 
5713601747802353 * 
100397446615566314002487 * 
3581874457050057021838729610409482762969149632972915379 * 
267535593139950330755907265689770024664090795106497661308268157342396003221



Sm91 C129=
(p55) * (p75)
by GNFS, 4 days

Submitted on Monday October 24, 2005 22:51







 1234567...92


Sm92 = (p1)^3 * p1 * p5 * p32 * p65 * p72 [ Length = 175 ]  (by Sean A. Irvine )



2^3 * 
3 * 
75503 * 
46731404628893905607210235741707 * 
17357685121487530272314084020479969142526171001787819150223751641 * 
839921864959969600234341350615454280584339900783049158479018433912354703



p32 by Sean A. Irvine

Sm92 C137=
(p65) * (p72)
by GNFS, 9 days

Submitted on Sunday January 22, 2006 21:28







 1234567...93


Sm93 = p1 * p2 * p4 * p10 * p29 * p52 * p82 [ Length = 177 ]  (by Sean A. Irvine )



3 * 
73 * 
1051 * 
3298142203 * 
19544056951015647623992763251 * 
4886013639051371332965225321191263200785903705285317 * 
1703057751798522700187996077196637285517155003415445664199429017748369723643706497



p29 by Sean A. Irvine

Sm93 C133=
(p52) * (p82)
by GNFS, 5 days

Submitted on Monday February 20, 2006 23:01







 1234567...94


Sm94 = p1 * p8 * p11 * p79 * p82 [ Length = 179 ]  (by Greg Childers )



2 * 
12871181 * 
98250285823 * 
1825097233762709447432521941926649289213154260264910537140594516431173070300371 * 
2674525573684858697560701870658348933916102325593721165422426453989766526938215889



Summary for Sm94(c160) = p79 * p82

The factorization was completed using SNFS. GGNFS was used for the sieving
and msieve for the post-processing.

Submitted on Sun, 9 Dec 2007 11:27







 1234567...95


Sm95 = p1 * p1 * p1 * p3 * p36 * p141 [ Length = 181 ]  (by Sean A. Irvine )



3 * 
5 * 
7 * 
401 * 
244987542265129586458446183157595351 * 
119684333324585760380296925278736677052991667067598465535119086641122308977254652550763964697554302296677991161440001789403458655109609795769







 1234567...96


Sm96 = (p1)^2 * p1 * p2 * p5 * p175 [ Length = 183 ]



2^2 * 
3 * 
23 * 
60331 * 
7414218343605898007054904008539678229463872328651811494111562828507144051357405695052612835346584059319708614758837877621899193657692066488505067022654601125869790297498349041







 1234567...97


Sm97 = p2 * p183 [ Length = 185 ] semiprime



13 * 
949667608470093318578167063015547864032712517561002409487257972106456954941803426651911500396348881197366045850894335742820591305439790288275136759985244833729682214530699379184227669







 1234567...98


Sm98 = p1 * (p1)^2 * p2 * p2 * p3 * p16 * p39 * p58 * p69 [ Length = 187 ]  (by Philippe Strohl )



2 * 
3^2 * 
23 * 
37 * 
199 * 
1495444452918817 * 
381502754125464943168932369122248696781 * 
3588472635471667861938967869443938442910813342994227048889 * 
197825482406769698151783117995020967519766027202915861687264259155363







 1234567...99


Sm99 = (p1)^2 * p5 * p12 * p65 * p107 [ Length = 189 ]  (by Greg Childers )



3^2 * 
31601 * 
786576340181 * 
37726668883887938032416757819314355053940153680075342644295667759 * 
14627910783072606795565990651314126145674770336615677946549896262532933945988541999815567058347827465728809



Summary for Sm99(c177) = p65 * p107

I finally got around to factoring Sm99 by SNFS. As for Sm94, I used
the GGNFS lattice siever and msieve for the postprocessing.

Submitted on Tue, 20 May 2008 4:35







 1234567...100


Sm100 = (p1)^2 * (p1)^2 * (p1)^3 * p4 * p7 * p10 * p20 * p30 * p118 [ Length = 192 ]  (by Sean A. Irvine )



2^2 * 
5^2 * 
7^3 * 
8171 * 
1065829 * 
2824782749 * 
20317177407273276661 * 
970447246795177523033247400823 * 
7420578382899399028284464392651452937744039836185355778662961413780805734369643748805299589898776112804950234221784569







 1234567...101


Sm101 = p1 * p4 * p21 * p61 * p109 [ Length = 195 ]  (by Bob Backstrom )



3 * 
8377 * 
799917088062980754649 * 
1399463086740105394672913130945493026937913499238148790743003 * 
4388325012701307167526588635576876644759452668196597056747408345988387366211263062577487913664612635611915493



Summary for Sm101(c169) = p61 * p109

Hello Patrick,

Here's another wanted number for your tables:

Sm(101) = 3 * 8377 * 799917088062980754649 * C169
Tue Jun  5 01:18:11 2012  prp61 factor: 1399463086740105394672913130945493026937913499238148790743003
Tue Jun  5 01:18:11 2012  prp109 factor: 4388325012701307167526588635576876644759452668196597056747408345988387366211263062577487913664612635611915493
Tue Jun  5 01:18:11 2012  elapsed time 04:27:08
(Just the elapsed time for ONE sqrt - it only took one, luckily).

The whole number took many weeks on various machines. The relations were slow coming because the Snfs coefficients were pretty dreadful
as you can see from the Msieve log below.
Mon Jun  4 20:51:03 2012  Msieve v. 1.44
Mon Jun  4 20:51:03 2012  random seeds: 4714fab8 a98d82fd
Mon Jun  4 20:51:03 2012  factoring
6141298867893783540378996188437492127764003798590081909642744192552148805391571094462286943973793319/
310495244779697771718230720369645297842348701438176773337763517045479 (169 digits)
Mon Jun  4 20:51:04 2012  no P-1/P+1/ECM available, skipping
Mon Jun  4 20:51:04 2012  commencing number field sieve (169-digit input)
Mon Jun  4 20:51:04 2012  R0: -10000000000000000000000000000000000000
Mon Jun  4 20:51:04 2012  R1:  1
Mon Jun  4 20:51:04 2012  A0: -8919910099
Mon Jun  4 20:51:04 2012  A1:  0
Mon Jun  4 20:51:04 2012  A2:  0
Mon Jun  4 20:51:04 2012  A3:  0
Mon Jun  4 20:51:04 2012  A4:  0
Mon Jun  4 20:51:04 2012  A5:  12099999899800
Mon Jun  4 20:51:04 2012  skew 1.00, size 3.077673e-16, alpha -0.346420, combined = 6.775396e-13

Kind regards,
--Bob.

Submitted on Mon, 4 June 2012 18:44







 1234567...102


Sm103 = p1 * p1 * p2 * p2 * p4 * p5 * p5 * p10 * p172 [ Length = 198 ]



2 * 
3 * 
19 * 
89 * 
3607 * 
15887 * 
32993 * 
2865523753 * 
2245981950884772863770930273540385579914865629636627917458256811732689892492870743326877749976350147897124023992523914020180640624011740696205659507665744332920411510673767







 1234567...103


Sm103 = p3 * p4 * p16 * p71 * p110 [ Length = 201 ]  (by Sean A. Irvine )



131 * 
1231 * 
1713675826579469 * 
16908963624339537484508436321314327604030763349996047014668841426185197 * 
26420435289199660352290245657167852985476641946070651819895933156168339498719086012326404560442282402403559611



Summary for Sm103(c180) = p71 * p110

The factorization of the C180 after removal of the small factors was completed by SNFS using yafu.
The entire factorization took 6 months of otherwise idle time on a single 12-core machine.

Regards,
Sean A. Irvine

Submitted on Mon, 15 February 2016 10:46







 1234567...104


Sm104 = (p1)^6 * p1 * p2 * p3 * p20 * p69 * p109 [ Length = 204 ]  (by Sean A. Irvine )



2^6 * 
3 * 
59 * 
773 * 
19601852982312892289 * 
117416055745722199032551613030131955173140365000320768767578421207867 * 
6125726861692155074440026231293274444423805613657273299528150618521012506340221515290231138888396870065232607



Summary for Sm104(c177) = p69 * p109

I completed the factorization of the remaining C177 of Sm104 by GNFS after 6 months of sieving
and 17 days linear algebra.
The entire computation was done with yafu running on a single 3.4 GHz i7-2600 machine.

Regards,
Sean A. Irvine

Submitted on Sat, 21 March 2020 2:18







 1234567...105


Sm105 = p1 * p1 * p3 * p13 * p44 * p146 [ length = 207 ]  (by Sean A. Irvine )



3 * 
5 * 
193 * 
6942508281251 * 
90853974148830729568788807471204169448373857 * 
67609243102773972838875424854217967300371972209133190536893586620791162850744838052281507779485845273498264830080938632761526794830712920440816557



Hi Patrick,
It has been a long time between drinks, but I finally factored another of these numbers
Sm105(c190)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=982310399
Step 1 took 63945ms
Step 2 took 30405ms
********** Factor found in step 2: 90853974148830729568788807471204169448373857
Found probable prime factor of 44 digits: 90853974148830729568788807471204169448373857
Probable prime cofactor 67609243102773972838... ...94830712920440816557 has 146 digits
Sean.

Submitted on Wed, 22 Dec 2010 19:43







 1234567...106


Sm106 = p1 * p2 * p3 * p3 * p29 * p35 * p69 * p71 [ Length = 210 ]  (by Sean A. Irvine )



2 * 
11 * 
127 * 
827 * 
95383501607400293616004374931 * 
54259599094002572583355411045946413 * 
375159085605310877928459072269605386653376782374874196433925741599663 * 
27518056325201854933261643718251313697576510084474601978478694683051383



by GNFS, 7 days
Finally did another of these numbers, sorry but it is not the most wanted Sm101.

Submitted on Wed, 29 Apr 2009 17:50







 1234567...107


Sm107 = (p1)^3 * p12 * p199 [ Length = 213 ]



3^3 * 
536288185369 * 
8526150295974562563911703097396807303361305853752080385827103422281006173895434732314352853475423512542010066856002013066381244223149688686332747287256098942256562363655334309484941298623600483738889







 1234567...108


Sm108 = (p1)^2 * (p1)^3 * p18 * p36 * p161 [ Length = 216 ]  (by Sean A. Irvine )



2^2 * 
3^3 * 
128451681010379681 * 
132761751746390611923240080737166083 * 
67031425578179280405553486489006742336953759049830840809351016348413007664845819742768984976575205426833399525010462614317613333284615639359796130220299502987337







 1234567...109


Sm109 = p1 * p4 * p8 * p20 * p31 * p67 * p90 [ Length = 219 ]  (by Unknown )



7 * 
1559 * 
78176687 * 
73024355266099724939 * 
9943216978062352390003139833531 * 
1330054388136326845371542874560114721263427298182714056642677810603 * 
149840603084337475988993463236995110967352586095183241932010459722363567237123276130962657



p31 by Sean A. Irvine







 1234567...110


Sm110 = p1 * p1 * p1 * p4 * p20 * p197 [ Length = 222 ]



2 * 
3 * 
5 * 
4517 * 
18443752916913621413 * 
49396290575478070579962193789705514377113696579391181438562209557211046308140914955475375292377669698324210580411428837724109733589770430705239901861854012027457023299672370583841892589110518827197







 1234567...111


Sm111 = p1 * p3 * p3 * p6 * p6 * p9 * p10 * p12 * p13 * p17 * p19 * p23 * p109 [ Length = 225 ]



3 * 
293 * 
431 * 
230273 * 
209071 * 
241423723 * 
3182306131 * 
171974155987 * 
1532064083461 * 
59183601887848987 * 
8526805649394145853 * 
27151072184008709784271 * 
2440480034289871822370862693886835126099170952229129167119083277062899175394632300484951689048576681026896223 







 1234567...112


Sm112 = (p1)^3 * p5 * p6 * p9 * p17 * p23 * p169 [ Length = 228 ]



2^3 * 
16619 * 
449797 * 
894009023 * 
74225338554790133 * 
10021106769497255963093 * 
3104515050823723908076909137590343647825269545315652029790926783188211767084523827184031625338265911008653113512314794480936566758254656863951748098953803988065923879729







 1234567...113


Sm113 = p1 * p2 * p2 * p4 * p7 * p8 * p18 * p37 * p75 * p83 [ Length = 231 ]  (by Sean A. Irvine )



3 * 
11 * 
13 * 
5653 * 
1016453 * 
16784357 * 
116507891014281007 * 
6844495453726387858061775603297883751 * 
274083639473114418810098845553160469060803472020901711735885001850493035179 * 
13652330611204925298260606291932608056492271043478425764831204949788104223444207523



Summary for Sm113(c157) = p75 * p83

" The entire computation of Sm104(C157) was done with yafu running on a single 3.4 GHz i7-2600 machine ".
Further, I also factored the remaining C157 composite of Sm113 by GNFS in 1 month using a similar machine.

I believe Sm114 is next smallest unfactored number of this form.

Regards,
Sean A. Irvine

Submitted on Sat, 21 March 2020 2:18







 1234567...114


Sm114 = p1 * p1 * p1 * p6 * p31 * p34 * p47 * p53 * p63 [ Length = 234 ]  (by Sean A. Irvine )



2 * 
3 * 
7 * 
178333 * 
2042059881000388200555074336219 * 
8678622406220213516465050301044327 * 
24075568431816864297632248860777423507383641907 * 
62041046777207692242447572091924037212783315235431589 * 
622671572255303237737485133617360962819046403525686867675770351



Summary for Sm114(c162) = p47 * p53 * p63

"The third to last factor (47 digits) was found by ECM with b1=11e7, leaving an easy C116 by GNFS to finish it off."

Submitted on Wed, 29 April 2020 6:05







 1234567...115


Sm115 = p1 * p3 * p3 * p3 * p5 * p8 * p18 * p50 * p152 [ Length = 237 ]  (by Sean A. Irvine )



5 * 
17 * 
19 * 
41 * 
36607 * 
71518987 * 
283858194594979819 * 
35876849722942437286649396513492746925705038271531 * 
69929007238910189440896360020171554156771275344878594027300265571638084469443386117564529410882181001246595145982221865975563979407080860715180311683161



Summary for Sm115(c202) = p50 * p152

GMP-ECM 6.4 [configured with GMP 6.0.0, --enable-asm-redc] [ECM]
Input number is 2508832483 ... 6758389491 (202 digits)
Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=1588162844
Step 1 took 1113195ms
Step 2 took 257537ms
 ********** Factor found in step 2: 35876849722942437286649396513492746925705038271531
Found probable prime factor of 50 digits: 35876849722942437286649396513492746925705038271531
Probable prime cofactor 6992900723 ... 0311683161 has 152 digits

Submitted on Sun, 8 November 2020 22:46







 1234567...116


Sm116 = (p1)^2 * (p1)^2 * p4 * p37 * p198 [ Length = 240 ]  (by Sean A. Irvine )



2^2 * 
3^2 * 
2239 * 
9787002048140152171263515060558503699 * 
156497968367245515655059056455089617073959013222149265770586804523805308165572520510050272136981198250507087284878063256342705928229557508508670247743582143974583381133763456377474127925121483818271







 1234567...117


Sm117 = (p1)^2 * p5 * p12 * p20 * p35 * p42 * p130 [ Length = 243 ]  (by Sean A. Irvine )



3^2 *
31883 * 
333699561211 * 
28437086452217952631 * 
29899433706805424728763564400367447 * 
319505907958401958357051507462193336760619 * 
4746032403816815975214853624607036716257319634142438753425546024369121494473738828190063585349428105104156771415393005556040837247



p35 by Philippe Strohl

Summary for p35 of Sm117

Philippe Strohl found a new factor of Sm117 (but the cofactor is still composite) :

Input number is (above) c206
Using B1=50000000, B2=288591693406, polynomial Dickson(12), sigma=759744520
dF=65536, k=6, d=690690, d2=17, i0=56
Expected number of curves to find a factor of n digits:
20	25	30	35	40	45	50	55	60	65
2	5	14	51	223	1139	6555	42004	296146	2292504
Step 1 took 1567405ms
Step 2 took 365869ms
********** Factor found in step 2: 29899433706805424728763564400367447
Found probable prime factor of 35 digits: 29899433706805424728763564400367447
Composite cofactor 
1516385392381488800257172455421115218103131389426237636403907504872104848630821256747576627427151045/
955402969807173970504574397911322632329216437824800943241454211577975893 has 172 digits

Submitted on Friday 22/08/2008 14:59

Summary for Sm117(c172) = p42 * p130

Unexpectedly, the next one came out rather quick,  here is the rest of Sm117:

Run 657 out of 4590:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3332531727
Step 1 took 35672ms
Step 2 took 13620ms
********** Factor found in step 2: 319505907958401958357051507462193336760619
Found probable prime factor of 42 digits: 319505907958401958357051507462193336760619
Probable prime cofactor 4746032403 ... 6040837247 has 130 digits

Sean.

Submitted on Mon, 9 November 2020 10:42







 1234567...118


Sm118 = p1 * p2 * p11 * p20 * p40 * p59 * p115 [ Length = 246 ]  (by Sean A. Irvine )



2 * 
83 *
33352084523 * 
20481677004050305811 * 
5747203274595182101743782698650656863747 * 
38736194414035077015862227517019570665653714001970285448031 * 
4890405641955581530316483984640301950064909595593296445634478042384514510212369135301909949580873481446130666608313



p40 submitted to factordb.com on 4 November 2018 (communicated by Alex Latham on Oct 17, 2022)

Sean A. Irvine finished running GNFS on the c174 for Sm118, after ca. four months of running time.

Submitted on Mon, 4 November 2023 9:13







 1234567...119


Sm119 = p1 * p2 * p3 * p3 * p4 * p39 * p201 [ Length = 249 ]



3 * 
59 * 
101 * 
139 * 
2801 *
165365274022584034353506983708790719561 * 
107262549014827605108170553542444185119309836220993508589614438998203997313532847379414499036635601582268738238072638661210529907049649737748338042860755091137808486160371905612311536822281399382425993



Summary for Sm119(c239) = p39 * p201

Submitted to factordb.com on 20 August 2021 (communicated by Alex Latham on Oct 17, 2022)







 1234567...120


Sm120 = (p1)^4 * p1 * p1 * p2 * p8 * p40 * p57 * p145 [ Length = 252 ]  (by Sean A. Irvine )



2^4 * 
3 * 
5 * 
13 * 
16693063 * 
1024001412736320019392148995069160443859 * 
279576210246975591413879862591888691573777646278467665473 * 
8279871212684048932811865452420379047357376308108739348862728517513525996252897386381120699815551355652654310647683079460112202910478437779699811



p40 submitted to factordb.com on 23 August 2021 (communicated by Alex Latham on Oct 17, 2022)

Sean A. Irvine has completed the factorization of the remaining c202 for Sm120 with ECM:

Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=1:1717354337
Step 1 took 224646ms
Step 2 took 75326ms
********** Factor found in step 2: 279576210246975591413879862591888691573777646278467665473
Found prime factor of 57 digits: 279576210246975591413879862591888691573777646278467665473
Prime cofactor 8279871212684048932811865452420379047357376308108739348862728517513525996252897386381120699815551355652654310647683079460112202910478437779699811 has 145 digits

Submitted on Thu, 10 August 2023 21:29







 1234567...121


Sm121 = p9 * p33 * p214 [ Length = 255 ]  (by Sean A. Irvine )



278240783 * 
105299178204417486675841093021769 * 
4213754301973277818574830150933029703205115128282586723382785882706969263182976786615125991432774212665571280081392800541558354419799245310412621791925662551088708112110138158616156416375634374522084788731721938623







 1234567...122


Sm122 = p1 * p1 * p2 * p9 * p14 * p233 [ Length = 258 ]



2 * 
3 * 
23 * 
618029123 * 
31949422933783 * 
45306856641154521457766703270320242968763335849955546717684945081881187367338244144043437588658869218015907458822474001579325203473863284859671581548238274058627446886736975249452833365841005182926249382278321304570156703240708360441







 1234567...123


Sm123 = p1 * p1 * p2 * p6 * p10 * p16 * p29 * p31 * p66 * p103 [ Length = 261 ]  (by Mehrshad Alipour )



3 * 
7 * 
37 * 
413923 * 
1565875469 * 
5500432543504219 * 
12347002211187670552593982429 * 
2829927788416784955921382453753 * 
490603365766589761252788965584567538918689227625761502090641756359 * 
2599877785756834172022406612564836069586385438389342330277037342180578839138482051324007676975879994901



p29 and p31 found by Sean A. Irvine on 3 August 2005 (see Messages)

Summary for Sm123[c169] = p66 * p103

The factorization was submitted to factordb.com on 5 May 2024 by Mehrshad Alipour from Iran.
Mehrshad used the application cado-nfs to factorize c169 on a core i3-12100 machine starting
with 16GB of ram. That seemed not enough, so he upgraded to 64GB, only to find out that 32GB was enough.







 1234567...124


Sm124 = (p1)^2 * p6 * p16 * p47 * c195 [ Length = 264 ]



2^2 *
739393 *
1958521545734977 * 
36193142873757992283586315838389993670506175189 * 
588877553843538799713765306327801633937621519940786897171404658557267917294998835137411559467118303182766629323132762988786937564320755535254244869454947966182720042357960885486699110417389933289



p47 submitted to factordb.com on 23 August 2021 (communicated by Alex Latham on Oct 17, 2022)







 1234567...125


Sm125 = (p1)^2 * (p1)^3 * p4 * p13 * p24 * c224 [ Length = 267 ]



3^2 *
5^3 *
4019 * 
7715697265127 * 
295999706346724665505289 * 
11955782051578068870996715574113327579491930757843833929238411263341491346956518715403679155140414913709005653897587053549582183867657144773717207515691678321060898354418349891914476834296835485120424057740487394866072756061



p24 by Sean A. Irvine







 1234567...126


Sm126 = p1 * (p1)^2 * p2 * p3 * p5 * p20 * p241 [ Length = 270 ]



2 * 
3^2 * 
29 * 
103 * 
70271 * 
11513388742821485203 * 
2838101657660281121635838482974785973172167634896902551225760546451986983167250817906190353710808248210766825163587350127671515116185896138062902354614719664032678541176075402608400798508031875431084629720784104890703458832231455912845908997







 1234567...127


Sm127 = p2 * p3 * p4 * p20 * c245 [ Length = 273 ]



53 * 
269 * 
4547 * 
56560310643009044407 * 
336705404741718452285011996925008237983156298846751623241302417011439351512564751598258632876057850530172766665240704250459291142219371648485922051590024341491094563539601763084457941803051106303965794068147883280296718180327425940329546813







 1234567...128


Sm128 = (p1)^3 * p1 * p1 * p2 * p2 * p6 * p22 * p37 * c206 [ Length = 276 ]



2^3 * 
3 * 
7 * 
11 * 
59 * 
215329 * 
8154316249498591416487 * 
6532897159547245195514315108364288167 * 
98710898075961375591497576343869714560966518634525903244905883607415709511772198694915446957053353657200532766380047193644750347571820095362243784257001037933159988823119601450482070667441278561741520802319



p37 submitted to factordb.com on 23 August 2021 (communicated by Alex Latham on Oct 17, 2022)







 1234567...129


Sm129 = p1 * p2 * c277 [ Length = 279 ]



3 * 
19 * 
216590858072126546342388979284247758463601100496368970584813221708490182706025342920611394827237464132732606948449585344853819069661706556975031190873827769096243312085948981217455433298068596668600180884394922994926507210721249321252833537
0475756475791598633739019739054861897







 1234567...130


Sm130 = p1 * p1 * p12 * c269 [ Length = 282 ]



2 * 
5 * 
166817332889 * 
740071711752279910983019901841593591648354166865247904157453792498389691374311212656163491454209390262070838164677567905044297208414725870301513275011714771337094973862269224701377289863230095375764361913248848544286050290270877878944285487
88712386545342905816900184217







 1234567...131


Sm131 = p1 * p2 * p2 * p4 * p11 * p12 * c256 [ Length = 285 ]



3 * 
19 * 
83 * 
1693 * 
23210501651 * 
575587270441 * 
115374375622583204904626854763579378161681853367824843538204694489322440978846825705379514910738068110360614417250486541312628796378285948125088504493116857699550355498755996568827733438394219834563218985157890363976341096338717600242843577
5463258992823927







 1234567...132


Sm132 = (p1)^2 * p1 * p2 * p13 * p40 * c233 [ Length = 288 ]



2^2 * 
3 * 
79 * 
2312656324607 * 
2540283627438011189845145124230082384829 * 
22167327235734680246954535484159674257350229311619825971454555872005134356413350091925458264983364766604313638095683747947702394137604469363279931375761072570287699886944053701726478970874854873078943899736212491323470043614941916953



p40 submitted to factordb.com on 23 August 2021 (communicated by Alex Latham on Oct 17, 2022)







 1234567...133


Sm133 = p19 * c272 [ Length = 291 ]



8223519074965787731 * 
150126470159158411307354179427311909786914154368133057691312700814270531804867102727595499538987896919299489741052249203939541976424727007104548147059468454650509456337270881012305602988590501033242133410293709190605598108732774128883869352
34108358887029883282968579008743







 1234567...134


Sm134 = p1 * (p1)^3 * p2 * p4 * p16 * p28 * c243 [ Length = 294 ]



2 * 
3^3 * 
73 * 
6173 * 
5527048386371021 * 
1417349652747970442615118133 * 
647637238580596134413990886300825671550680475409685218179098924618498914927104640633532943345067820744812553228940215778123341572783466566042033295998510679182938541016629300843037698433762972565398466495051910740988433510616905148611907123
793







 1234567...135


Sm135 = (p1)^3 * p1 * p2 * p2 * p3 * p10 * p12 * p15 * c254 [ Length = 297 ]



3^3 * 
5 * 
11 * 
37 * 
647 * 
1480867981 * 
174496625453 * 
151994480112757 * 
884201662685354854162961490943984946862561136365041850271367084854547849535258115659320127178312884999919228692361705210800628973255564980721192533025579132697820992767814246183252506853608646901744760779307509528964724222125808559518799337
30483300768869







 1234567...136


Sm136 = (p1)^5 * p4 * p4 * p13 * p26 * c253 [ Length = 300 ]



2^5 * 
1259 * 
4111 * 
9485286634381 * 
10151962417972135624157641 * 
774089776410313692582963143248216990889359543901305539550575594212990653019739428528811986910012321273856511600990265329693201025273620175861191305564980593289797791957528815550315936969244873277097479121470596925993041811253406967627659675
8353772948387







 1234567...137


Sm137 = p1 * (p1)^2 * p13 * p30 * c258 [ Length = 303 ]



3 * 
7^2 * 
7459866979837 * 
144065103514544138702103468451 * 
781461818612935912244179550077619047624409137230897390960927211720319424489482120677056304543119202666345117064993923187797034738474116872610069940024770710458555402525815906735118829990247455514063749506571518448384576137944429510953795847
353376929543475333



p30 by Sean A. Irvine







 1234567...138


Sm138 = p1 * p1 * p3 * p5 * p6 * p15 * c277 [ Length = 306 ]



2 * 
3 * 
181 * 
78311 * 
914569 * 
413202386279227 * 
384134297539886771745157582011666871416171008362507862601104573416627494921896979465320508666644777197086681865142822466426671043899514977282744754378183884195577205642799029159495681020641145782569215536253978369362749427322571742832444712
7238477150642009708211085821751772731







 1234567...139


Sm139 = p2 * p11 * p12 * p12 * p22 * p37 * p215 [ Length = 309 ]



13 * 
62814588973 * 
115754581759 * 
964458587927 * 
9196988352200440482601 * 
2662520919727992778114192625316520801 * 
55303251118984373249719165791340201877773320666711687179919506291237507133144359434557545077885351236962474986502203967588520562972438544696550056777370734171639162749148850530316319312049593515270674597150927754227



p37 submitted to factordb.com on 20 August 2021 (communicated by Alex Latham on Oct 17, 2022)







 1234567...140


Sm140 = (p1)^2 * p1 * p1 * p2 * p3 * p4 * p5 * p11 * p18 * p23 * c248 [ Length = 312 ]



2^2 * 
3 * 
5 * 
23 * 
761 * 
1873 * 
12841 * 
34690415939 * 
226556543956403897 * 
10856300652094466205709 * 
572857536199494174553472060884991021196252030246440267253089355048901533389268822589986492945490993840333040443467034288047970883561484316580158280419398112514033176528197798372329409768901398456695157755890812961156323240437923070144890424
36853463







 1234567...141


Sm140 = p1 * p6 * p309 [ Length = 315 ]



3 * 
107171 * 
383986927748215877476685913764050667700070066476099918925031138317391222570889654429987263505753591785270225342727241656065779205528774069713410589301464725796029049802001534289280983910134582741917443786425762277444797286924983167443043099
710176941896971886434216112960058001166765048791598268608535695720357







 1234567...142


Sm142 = p1 * p1 * p4 * p5 * p5 * p22 * c282 [ Length = 318 ]



2 * 
7 * 
4523 * 
14303 * 
76079 * 
2244048237264532856611 * 
798428869689961124854550782227208206273280990815818701909134575585798799012842305146271145428913184008743313408308740113445618126241703975768157709038561029940687370106599765807432072305730054753607196825725385032893725258315522226903933141
997489082505346965529222057364249227244973







 1234567...143


Sm143 = (p1)^2 * p3 * c317 [ Length = 321 ]



3^2 * 
859 * 
159690582202964857605952293612755429212589092333372543310494808399740530516665949378797691180345821440509100970917428077307821588031525983023887956018732154164867013179395834036928724589185228432417673139445228440186404229868208657501119022
27023427644563591013209691518060681429198050851394791635640426482749856440453







 1234567...144


Sm144 = (p1)^2 * (p1)^2 * p4 * p13 * p14 * p21 * p271 [ Length = 324 ]



2^3 * 
3^2 * 
6361 * 
6585181700551 * 
81557411089043 * 
165684233831183308123 * 
302931689993912862383229276114787027281405114796886618094086589746232331834212621096315668911107376877078295312200829930661169651615343618354721976565378756498778447770707406136218366476787471181094421056805395804695142359050642416127994721
1076715922035883967781648857763







 1234567...145


Sm145 = p1 * p8 * c318 [ Length = 327 ]



5 * 
96151639 * 
256796015928781268960296596071589008117173389593349133098695356350273767340428685702899968354206327269486453497930001269279823445770222881953718498335908404816393588234082872563305128849439789791003153059315205447736796478552200473907917713
429966844600789638381773450842844453497314031500041583555608734112455722447211







 1234567...146


Sm146 = p1 * p1 * p2 * p2 * p12 * p19 * c296 [ Length = 330 ]



2 * 
3 * 
13 * 
83 * 
720716898227 * 
1122016187632880261 * 
235818816245539713600331981587715785788524823275091489592452248030557841504828966423942497595543800995982128928947575522035526321290583995004579719700822772682600721229040541590622379858203374604761120936537888169703192813046776187209261825
37034382300824024667214545220707793570241011633788755207







 1234567...147


Sm147 = p1 * p5 * p22 * p31 * c276 [ Length = 333 ]



3 * 
59113 * 
1833894252004152212837 * 
1519080701040059055565669511153 * 
249893860720970494660634402277189581860549347857029659352882266281982140619591595175164744201005542378361314264168974568464619893796710116738490423551159286776817143982445018286530486370621230721463856257491419478839889336250857686273580085
622742942302372787167916598094915093







 1234567...148


Sm148 = (p1)^2 * p3 * p5 * p5 * p6 * p6 * p13 * p13 * p34 * p254 [ Length = 336 ]  (by Sean A. Irvine )



2^2 * 
197 * 
11927 * 
17377 * 
273131 * 
623321 * 
3417425341307 * 
4614988413949 * 
8817212782626223819399721069204897 * 
319300070156852478246718889830464122077571283705311623132323743476820895657676871869020093470476964497764322177957871760330493034912815489120806404979668011225719250826344570989463507211375055519415190119868082433415218699761826055025612259
15860092642869







 1234567...149


Sm149 = p1 * p3 * p3 * p4 * c331 [ Length = 339 ]



3 * 
103 * 
131 * 
1399 * 
218005518831775286892220693280915331832422938462254589272983429390587747715450661786063453849101531242812611967783476299771065065722131756483034494660680361931168552313336782900304233819135050234312766352918628069165010454614977978087165160
9522750606874407386894407750358278911837926871675466385373538882923085051171657273064013869







 1234567...150


Sm150 = p1 * p1 * (p1)^2 * p2 * p2 * p16 * p26 * c296 [ Length = 342 ]



2 * 
3 * 
5^2 * 
11 * 
23 * 
2315007810082921 * 
92477662071402284092009799 * 
151954615147351455095110171852352613079653903481393655907561645565943483369431384166253265727397630989754924090769984676181814684321838064669502503815963810062634297111660745087962800954144852613451217337413083025689750684296077069060732783
30637748385315835235144059764059612685623536281382927503







 1234567...151


Sm151 = p1 * p2 * p4 * p4 * c335 [ Length = 345 ]



7 * 
53 * 
1801 * 
3323 * 
556028450455378906419549862887664624216859834610752656822523083975961916967920924042850190210814971110936378324496736009717140694715000056821531441497934729954707133637288052170296970957404914191065131035752999884986622675900738108656350421
57728347098279107910029663171640821794586869438170757815204918091255373015675237077975233874447







 1234567...152


Sm152 = (p1)^4 * (p1)^2 * p3 * p5 * p20 * p22 * p31 * p32 * p32 * p205 [ Length = 348 ]  (by Sean A. Irvine )



2^4 * 
3^2 * 
131 * 
10613 * 
29354379044409991753 * 
2587833772662908004979 * 
4103096315830350734534473515557 * 
12805089500421274253268517941967 * 
17815076027044127272632744936161 * 
8672648427724666836335878649605123533671234498113722493001839423884394310675246313883662523667972796225220735409952709165862130017818166129799353719223483490503275166918260572071118186769070106198500506817







 1234567...153


Sm153 = (p1)^2 * p2 * p4 * p7 * p7 * p9 * c322 [ Length = 351 ]



3^2 * 
29 * 
7237 * 
6987053 * 
8237263 * 
389365981 * 
291662721014734703170595264452931192413345222129502917962456593142482468756674368499704879388193619235970327807465985644040573575289839791982794486031875237070876729415843686066457407897951275102408749386102467915352964244073766628873594128
1200381311694470835474221652767087655442802101924633966639113856928724902506353031







 1234567...154


Sm154 = p1 * p2 * p2 * p2 * p18 * p21 * p32 * c279 [ Length = 354 ]



2 * 
17 * 
19 * 
43 * 
444802312089588077 * 
855286987917657769927 * 
32063206397901252963254536935569 * 
364357868151023104065690014392869296210548056261116243234467027829933297505578352030641966675499413252868435017382566068584271649811907764798030137051147261948778664806775328763343536767857383585802163855622996879404308912106199251738632133
631036988979348920693263712626113446243



p32 by Sean A. Irvine







 1234567...155


Sm155 = p1 * p1 * p9 * p24 * p323 [ Length = 357 ]



3 * 
5 * 
665009999 * 
223237752082537677918401 * 
554405975361398849086315094251866436826149186233995916322648863211855040945417732420881665849442175218073101972058302322367513350203978349990409656089950991903311063087768208087655812903149437572283142094574622685970434438853115676471655863
94732777654606357440424620177768705937886072566917369570519043697226934404184296523







 1234567...156


Sm156 = (p1)^2 * p1 * p1 * p4 * c354 [ Length = 360 ]



2^2 * 
3 * 
7 * 
3307 * 
444428085810445848687350490993207850318417740445700725853325328573730341636191791815155784452623419858516516050427893381163609910101130133323857685710260444601129954818030005953999441948173067595080072228120387155341876215355278532960801460
527877802929288241835947287593874206694062130589273597618097747700185537680325079356002225247844216273385287172787







 1234567...157


Sm157 = p2 * p2 * p6 * p8 * p12 * p18 * c318 [ Length = 363 ]



11 * 
53 * 
492601 * 
43169527 * 
645865664923 * 
125176035875938771 * 
123171562836153566068957324589265381565397200006993644472677662947419327821108690678960820685810830317459667900820066018147149358545252745157761989566806866502588364923606853126753693645014338621771464893122776977411815508084552766667202431
657516180225309291242630464351473412595422593795161392959158351372056609357669







 1234567...158


Sm158 = p1 * p1 * p2 * p2 * p8 * p21 * c334 [ Length = 366 ]



2 * 
3 * 
17 * 
29 * 
53854663 * 
164031369541076815133 * 
472461673917671792105317513599604927664704742613889071872507044016561219352623852114255155374993904236374485314532495024374124185919007147881270097540813614075468629948463178857820486606814500407661441815131112776560582298359589940029000432
2478992176999471111543050860603885776920143088996841845389885280574199247401746496842934843519







 1234567...159


Sm159 = p1 * p2 * p3 * p10 * p25 * p32 * p38 * c261 [ Length = 369 ]



3 * 
71 * 
647 * 
3175105177 * 
1957802969152764074566129 * 
11855111297257593607972759339201 * 
45941358846148651407783221723920871719 * 
264602852938896854658792238839624264257227720584770327380191939141444501695531301016572569666318193692536121526266335701564755783626175997269133907697855056392892412943072813878004724885082914162981075053940022130859199511425477323866542802
507239213817360628747



p32 by Sean A. Irvine

p38 submitted to factordb.com before November 4, 2018.







 1234567...160


Sm160 = (p1)^3 * p1 * p2 * p6 * p6 * p8 * p27 * p32 * c292 [ Length = 372 ]



2^3 * 
5 * 
37 * 
130547 * 
859933 * 
21274133 * 
122800249349203273846720291 * 
64603936118676024484144135734907 * 
440262457055513843388420187113234615175539026557285007915212958926035750460796131607770797636416464742586933863254729469894378005856037206329537366657963179350321131804864209307357231697508442628918674169893694027939483607973600783194622060
8343717739966765078765180632177404530263379499117877



p32 by Sean A. Irvine







 1234567...161


Sm161 = (p1)^4 * p2 * p3 * p8 * p360 [ Length = 375 ]



3^4 * 
59 * 
491 * 
81705851 * 
643936877262798276809635056823437176599393889312742534497858808401753128376387988973593769339663303074973747362480368159636806324001422178459069558417749689063473399179492414686898291521605975723614710064627963449867860721592074010892366031
555385848957957814583492377279631045136591702621255249517529486990821313347343984837578614067656268464133530164155430699







 1234567...162


Sm162 = p1 * (p1)^5 * p4 * p21 * p26 * c325 [ Length = 378 ]



2 * 
3^5 * 
2999 * 
393803780657062026421 * 
22260247937572504750086047 * 
966256356744337186813716438702029991240981869552730990577342121545852624144032531193978476954880363092560643243407536698394784819429029461996401613001373819470855425200715281560745361889795571079780911200452959631077051186405319582536638396
2910424248139920421207225113340568687828821563236607127519116419856244591389453966259



p26 by Sean A. Irvine







 1234567...163


Sm163 = p4 * p11 * p12 * p25 * c330 [ Length = 381 ]



2381 * 
72549525869 * 
666733067809 * 
1550529016982764630292633 * 
691335900725482080926917327062976539204766778306445304306865702181369731538361534632243829486752179341455231055622553838521294888867369456421187293017360639461294096828185536793711361401395360250892938068201952066269448631904818275686743871
673666548396517255969560532102847984782998980743506213320593123686023459761093650116039411







 1234567...164


Sm164 = (p1)^2 * p1 * p34 * c349 [ Length = 384 ]



2^2 * 
3 * 
1039418554780603268384723777072953 * 
989790466132055809201598724528734111805917730992528043185856800614231631401248702785939536339220094829967353922370866655803401211500643473347187680255000891403779620475087779288754227270393067481010476919021853118379746985450814950701004194
4117175183407038587950993904880534631736688265614558444741381814088317864257796204987978223422894902225701349







 1234567...165


Sm165 = p1 * p1 * p1 * p2 * p2 * p9 * p15 * p32 * p328 [ Length = 387 ]  (by Sean A. Irvine )



3 * 
5 * 
7 * 
13 * 
31 * 
247007767 * 
490242053931613 * 
13183356310254866666237435750357 * 
182756768194173135612106227451977729186376097283472414010936473228314943112176399502623782011430368154965927915015628712360221995550660112984516422314017356319293007617461998788639226078300814391329518357914807533066417404260975659341568447
5050607014396967804555792833912178431145501933981844058731687369979309788684753888188553







 1234567...166


Sm166 = p1 * p2 * p23 * p365 [ Length = 390 ]



2 * 
89 * 
55566524959746113370037 * 
124819298554773166559157445477277487337716282207978059721756572699958798452384754690990740475025356570275858324048001456345375082508297216418812977378322921989705015381981809816775570071353103697462706966273542556642092741015816112733351258
37066891409220213283241287036537487578933027111131002578906570041512881790750932046472049727896182641483362152927269462128531







 1234567...167


Sm167 = p1 * p4 * c389 [ Length = 393 ]



3 * 
3313 * 
124214497536082233036685499740437893474446752473015709058601002489022441032734123618823317286975907591968594386373139799342667139256638230682933674210767510197060758515938141959905017587180903613142270956942455083115111288973852614059880386
47461326000615869013293502880181821926665673722923144595546447040762565664668693343811766389691935722924957455795769710851912482056561139165224284653







 1234567...168


Sm168 = (p1)^7 * p1 * p6 * p387 [ Length = 396 ]



2^7 * 
3 * 
532709 * 
603522851971363056053086471460131641232657761647161378373243414272220133232696215753408594930216329782348267889419651716542028915466222028367855478231713927777146934588265861839504136032656803583107087547373357350061730026927186252221522034
647424957857508362343485359766694504572433323177563554355036283969742099565724747353391785680734331649209278234155881952734543699242149766194876903







 1234567...169


Sm169 = p4 * p4 * c391 [ Length = 399 ]



2671 * 
5233 * 
883263643892205631751053960627718889951063140418964557379349826171107084818870406662757686146253651753824642928318090545296605153834836402567839816180241326158045115505793334927457936604253756247536481748391708689613677721946954532875920095
2363987856642075831087791515606873790614577543967629193555322863446875428408828712591881457523661625113668037849121621767252771800775094534287680080983







 1234567...170


Sm170 = p1 * (p1)^2 * p1 * p1 * p3 * p14 * c382 [ Length = 402 ]



2 * 
3^2 * 
5 * 
7 * 
701 * 
73406007054077 * 
380824437250218390642711000487470435317764078406179828054713887071775626262999569231657076078241421333054393670747570497329417165047159309022971579965927198131584925118926270860822627577291033932783028680258488377265216404001474676750503257
1048077343859148582844187613558824620925360746281373753641688512508403218287638916088620430386196058562666232177613198392916656646285297946067







 1234567...171


Sm171 = (p1)^2 * p4 * p19 * p35 * c347 [ Length = 405 ]



3^2 * 
1237 * 
6017588157881558471 * 
40202471819457246557501649563881337 * 
458381995434290276780026329457306309599832028089258909410723788009960543250019282795503968692995316177770560873868121654523993391631745124897309167031353187113136545060015834532727481853999734192184998020873255164455971921071976556049381548
15818418717934999045768636798768946312086623752717198318776203091444825110534298458738806616172143489508281



p35 submitted to factordb.com before November 4, 2018.







 1234567...172


Sm172 = (p1)^2 * p2 * p2 * p2 * c403 [ Length = 408 ]



2^2 * 
11 * 
13 * 
37 * 
583333911836666657603296721754022029504123168035013765041313250679641864214866969687906327024784325059807153471065316795344343553709944894517897272718209357327814628090110183774095619825643073620781057947954574310660126205401210135674329597
9829810958236681256998871911081417885519284215277505865391047870824945196614162877723735879188629235973877913114446945575371298391616006528216035020136418832412123







 1234567...173


Sm173 = p1 * p2 * p2 * p3 * p3 * p5 * p6 * p39 * c355 [ Length = 411 ]



3 * 
17 * 
53 * 
101 * 
153 * 
11633 * 
228673 * 
150506237026606783276384195724025646577 * 
748131381129933879590510373849816923393987460494857491606649545299999121895690735175386027201795237421943151341727713686620027814552179874150770345217769065601428748483304891671658511419335997520062304865588797390864005061386010816512780531
4719361420934335522546432355759092516979844862275531567776653329478748352798561322609062898908629268360337241773573



Factor p39 found by scanning factordb.com

Date of submission of p39 → Between August 24, 2024, 1:20 am and August 24, 2024, 1:21 am







 1234567...174


Sm174 = p1 * p1 * p2 * p3 * p7 * p22 * p39 * p40 * c303 [ Length = 414 ]



2 * 
3 * 
59 * 
277 * 
2522957 * 
2928995151034569627547 * 
479507004180504565435047494228653196053 * 
1579762605250399847831834107529887281721 * 
224914088547286835858198690922489017011797386382052371124754674344935880492563379904569943721927887657718242343223353870122123434138346587530149524422141374150810581154824130203010012896613324838004842535873886660279455641442045032977874990
100776950310735761534424894540347157452836590115726184451504389



Factors p39 & p40 found by scanning factordb.com

Date of submission of p39 → August 15, 2024, 3:54 pm
Date of submission of p40 → August 24, 2024, 1:18 am







 1234567...175


Sm175 = (p1)^2 * p13 * c403 [ Length = 417 ]



5^2 * 
2606426254567 * 
189465232534072586430380437789305348621796984271461517764260313855410550439352656919592639943033811757687341257059150269560693765167920068477356749478808018707499792145974637281654226531167550908668989738930517712034538498675230549495379945
9789327486993728002787191548702358765087457496689540698887725334144913559171630312205829806249803247209927637936591025274501863974764846584005786565989449914377201







 1234567...176


Sm176 = (p1)^3 * p1 * p2 * p4 * p19 * p28 * c369 [ Length = 420 ]



2^3 * 
3 * 
19 * 
1051 * 
1031835687651103571 * 
1011379313630785579015894871 * 
246844132111589264774295918561288270010049003962486940960336738030267353753979092662351186496489931394287619228294826123320508008970637308623684665406250162349206113529819143311090877209337095517735125522715128522115121903624007157453687783
101184451167113574192627797148134289718072501213867999851602987775540007552311248123583917134628838942206588694961343202339141031



p28 by Sean A. Irvine







 1234567...177


Sm177 = p1 * p3 * p6 * p7 * p11 * p16 * c382 [ Length = 423 ]



3 * 
109 * 
153277 * 
6690569 * 
32545700623 * 
2984807754776597 * 
378980783869354890538816255367593075202190045751217621297869071239780345755165921020779119695885741103236195862450588874903945027110841023437085828489552963316325430858011521085926022200058916224740198499989255463685262286855781435939999629
3440402766775517800195161154573193192674724474116122408730657141905650547933629847903241569132651991594329540743608706808592370391581652873217







 1234567...178


Sm178 = p1 * p13 * p17 * p397 [ Length = 426 ]



2 * 
3144036216187 * 
11409535046513339 * 
172079642495898962119712019149827088042504874761467313828842743572736517221186780659959064616853777634881618576072376718877160473546754450767450623088053060230669445261102516543716228829003436778158472775178297406525014801821796893544680462
3840678229929925088293377235585961990200769128189780441052457501524916828668303939775759676867206470259475035320103878284258922951791050919791562775748396373







 1234567...179


Sm179 = (p1)^2 * p1 * p2 * p3 * c423 [ Length = 429 ]



3^2 * 
7 * 
11 * 
359 * 
496234888081419573430933763388043677218876497899529771384129943983565878210816664314246705219828023794079216199464858077659511428278699198413774750280689217623343212824588580970668069392287780716444601623497634953225486500947043507555117896
502301644057451241918284014543071495412260813998051080382560733230189439726119705387118885420653607906165322758641549422426244776295229100247055373336095407594328365920137202406782417







 1234567...180


Sm180 = (p1)^2 * (p1)^2 * p1 * p2 * p2 * p4 * c422 [ Length = 432 ]



2^2 * 
3^2 * 
5 * 
43 * 
89 * 
7121 * 
251676707884849271586469056114820416546044067619470872986836265328749404061380097363600377035468650171374739637213703309931350792802397006101444991714006354871395194208756754923804081397036986631962231024133786310814737893930745210617347374
29298710344943971920271451361862065999766413463881704853828383639087131780406100968444205259151769448075494634988840205559689627122832587374251926808211805277247445155500228085691053







 1234567...181


Sm181 = p2 * p3 * p5 * p20 * c406 [ Length = 435 ]



31 * 
197 * 
70999 * 
46096011552749697739 * 
617691287803957604354670479035303436880525007901231281260320058331189159370022184962600350466073568809354923730624285711086006496664449256635895885709227919057044800688848598345369015933183832367829892805340292153317586510051350836417671167
4914719627912121673905385266220378636560543997233035910127660226891146647601065876808661674207986783379855958430566520723383976510786416744649673628932518018146086203







 1234567...182


Sm182 = p1 * p1 * p9 * c429 [ Length = 438 ]



2 * 
3 * 
123529391 * 
166568711707256954764125349181099233736545374429596695781955697185510834074073979507096270786177186711861937861433402579966680250353230697240529285318128363995116875854792753051443977112430811575174180078468270636240877970640352995175206409
133189092788615682728660805273630694265477990756241881112509406955816612287222322046614728510437581004711599570062581511684073845443741619572900084383112744627673494550746461861825494871067







 1234567...183


Sm183 = p1 * p2 * p3 * p4 * p16 * p30 * p43 * c345 [ Length = 441 ]



3 * 
29 * 
661 * 
1723 * 
3346484052265661 * 
553245689211853052761209813199 * 
1059928219918207546246706395447867299870067 * 
634929834506526876297647680365724131074517856245427517727008884654744298625708996190269745160228134435109420333947158311288850145871753582149169954012020544705586301910346273444696237217565558542993989702120263259497191209785513334428224789
616365785577637370480947922046612441766948172723856700827493372568944315380995351699668212753548933652031



p30 by Sean A. Irvine

Factor p43 found by scanning factordb.com

Date of submission of p43 → June 28, 2024, 7:27 pm







 1234567...184


Sm184 = (p1)^4 * p1 * p2 * p3 * p4 * p4 * p11 * p17 * p18 * p19 * p27 * p342 [ Length = 444 ]  (by Sean A. Irvine )



2^4 * 
7 * 
59 * 
191 * 
1093 * 
1223 * 
22521973429 * 
15219125459582087 * 
158906425126963139 * 
2513521443592870099 * 
677008100402429325901609057 * 
789497757457178155644478620259361413972150672081760436601552877576067637316044253034501948330770097859300923037781520324045517956750901709230536602932308434986143596639398443656273661658327853053173654182408958317242742517820581180854453052
925226658686768857580470091786086406610221754789129568203967384451608838167466879488313009807568569387







 1234567...185


Sm185 = p1 * p1 * p8 * p13 * p16 * c409 [ Length = 447 ]



3 * 
5 * 
94050577 * 
4716042857821 * 
3479131875325867 * 
533351621984799969936162186866536516006398881165823993170915822324876528786193287723556035078086620884250934345842619491164243631630538572043211588172677044714775014150341345114863817926212892445158466139180663177538853890760364020235455026
7055385512856136507169703764079837433961386165083423151309476147627120057361209514039199017910453864732979322936673594217273723951595676820310077891234934325129397084761







 1234567...186


Sm186 = p1 * p1 * p4 * p21 * c425 [ Length = 450 ]



2 * 
3 * 
1201 * 
574850252802945786301 * 
298034124502074098101512668464482822908652542523273666028642684799238307322893078046907367202677614585558168699238971552745323664916104115985286964344522797611683828395310392532725464757984814175216673122414542074002937385454614948581222778
50919142186997475255773656256280391374441743491630892145619591257066811851741551542931599908954597575263175781858127461677445180342984555398523710492210530628444970003774434465773425031







 1234567...187


Sm187 = p3 * p9 * p31 * p411 [ Length = 453 ]  (by Sean A. Irvine )



349 * 
506442073 * 
1080829169904060835770214147747 * 
646253213525936563202131494265843172809473362059914914173432708236767129869232028235090059727829636553795408840233127105558561773084467674051729709389777726767967802284317022428165091134213394445922362621714833233212554723714564174418111669
498936207951085298551799080803363445759267522417246541605647908977558423780331081208797817453303153554382680801195027077476809337778612645835221413891384933392084296657173







 1234567...188


Sm188 = (p1)^2 * (p1)^3 * c454 [ Length = 456 ]



2^2 * 
3^3 * 
114311841760289010569594183511130761411345025261972512253095867012814263094846708763656013936597550514497764778348392265339515620099234016181266461850075767023017303600917517864768145351758426019538984355652876025100101027880659363994551033
4417760362223343723362260417834510445640093806779010501251260529056843890195760584668010612473593973612510668084760695890344057029260751501510779307094140446010834918260862723844223862760918335010946140594307279511







 1234567...189


Sm189 = (p1)^3 * p2 * p7 * p10 * p10 * p21 * c410 [ Length = 459 ]



3^3 * 
47 * 
1515169 * 
1550882611 * 
1687056803 * 
348528133548561476953 * 
704118583577713797078398658908003728031900843914139757832144494986126668190798285697306191950099948172947632501506555031819766524522062844214386799757731790508877127338472304589241744718275536202751889039042846243680487678897872217017430439
38470123426043480817060031301133574570669933659146087080803463673846761765910881774365387978938262570593602449691692182700835337880269663784311472845785615307729864408601







 1234567...190


Sm190 = p1 * p1 * p3 * p23 * p435 [ Length = 462 ]



2 * 
5 * 
379 * 
46645758388308293907739 * 
698334678474731226954203275220474188515870231140888920157380649749714630298163563890827583156235678406707150178926396065948318381061042152090125065337104586954721906199767370480826970612106279221187509703470514016996510705114927761279158607
800399519570000171100337592081033222510846868634882798195310888649733519205868329146977603967516107577069874382756235348861655882370697739050483812729273344054763850637031321826560460734714491999







 1234567...191


Sm191 = p1 * p2 * p4 * p12 * p20 * c429 [ Length = 465 ]



3 * 
13 * 
5233 * 
164130096629 * 
13806214882775315521 * 
266954214755806657783701473423485306938586062152607230052449979307325098257844629398194502635217917183182456273211216589853660356013322815793868770779953106120974798634815554092236537707402522742879243077382958327250723822564495930060837219
212743505119724423551387065633644991659252906850494873872085078946628642639294098329676357613123018172729123754334696906839700381847620698611068998052896832110315326273646505224537230670277







 1234567...192


Sm192 = (p1)^3 * p1 * p2 * p2 * c463 [ Length = 468 ]



2^3 * 
3 * 
29 * 
41 * 
432635229538520225032105824894944008705679237745059970680346006356319750989747846456225452241117726926190026495010736075717258444446217891350461798423331330196449004376895568033184738505393538341400697729552516495332594302323773875505029142
5466712893191797102716713103662991594096233919685069180513601665900586632364106502107693655282735812662992435981011885203152444601912011570057617226176309509713000111163904337509678202207007996256734762552046053658122693797







 1234567...193


Sm193 = p1 * p3 * p21 * p34 * p41 * c372 [ Length = 471 ]



7 * 
419 * 
419908232491384495189 * 
5167315927941164272437909427556797 * 
41947561597388645099154464763283147970849 * 
462462784607060066661518759364344846830192018578413654187078634592017634251771688572432349892109583794498042183827004477699906560468695479624483188320271461004366183550212629988361281797925835473782783398690746955092180762514918329948358909
349920389528280104216123793002821230989760020501324747333496224818584875152217321509543413494448890341061145582901802687850926716413



p21 by Sean A. Irvine

p34 submitted to factordb.com before November 4, 2018.

Factor p41 found by scanning factordb.com

Date of submission of p41 → May 29, 2024, 2:22 am







 1234567...194


Sm194 = p1 * p1 * p2 * p2 * p3 * p8 * p14 * p16 * p19 * p20 * p21 * c373 [ Length = 474 ]



2 * 
3 * 
11 * 
31 * 
491 * 
34188439 * 
28739332991401 * 
8203347603076921 * 
1507421050431503839 * 
22805873052490568609 * 
168560953170124281211 * 
263113134601433623506159251836470173818986318512714282934667360849921456133025826609027503552759240462919825207117836542620114188164780004461180452534576258311952733761630533028031272510138063018967189109162016573497133785379924297757292881
5960842229564148775574083899493815573787731753297181371675911056346444880131615129945020771988104129908002462227413731373835543197531







 1234567...195


Sm195 = p1 * p1 * p3 * p8 * p9 * p9 * p10 * p27 * p412 [ Length = 477 ]  (by Sean A. Irvine )



3 * 
5 * 
397 * 
21728563 * 
300856949 * 
554551531 * 
8174619091 * 
165897663095213559529993681 * 
421689179216004490268670579952138892539073288812243260875778257072007240866587533894580959087348349946204992973367677957665918840799383893405121462889149077964908152057144546772492950163139967315190731294500128685930803732434591580562083296
7849640928461423485497035455345542521700809846462266645935693244989301840859149448482745301257117142121991254187915811979621816086743861383233522991211424294391495728519167







 1234567...196


Sm196 = (p1)^2 * p2 * p2 * p2 * p10 * p464 [ Length = 480 ]



2^2 * 
17 * 
73 * 
79 * 
3834513037 * 
821005175270568520408869433983216434183114591112676333745917354072569340548280754450517350676544898072821012903517554104139527969078949989299158584226264083288003675945748232271428765749277016711848572198548409604596374222112190891021649595
27873452634755168414750187208738721246827545799527258680876722972354788603612965854168365101059553630090692414068147728426416538096588069005207407056015550690564626039305537870197599450267926525787128394411912946409886699293







 1234567...197


Sm197 = (p1)^2 * p2 * p4 * p16 * c461 [ Length = 483 ]



3^2 * 
37 * 
6277 * 
1368971104990459 * 
431443900763626419637033585824555393600876092546075819339404222959249147825370084733652776320031918376058550371663755075056369556138150692154781392442924982822285263343203764600469394128581001243598705961766402429514750746361475735661791263
22884259594122545071451008793369483883440188589800418022199814209811781249776856825241223978909027822664031031884374456913126173644842841830316461498361487023246089650234667575493207727752598714881267791711099478763328863







 1234567...198


Sm198 = p1 * (p1)^2 * (p1)^2 * p2 * p29 * c453 [ Length = 486 ]



2 * 
3^2 * 
7^2 * 
13 * 
14158849264684185910199571953 * 
760457735226784091294840569472145458786991928653508380971124951232445893341537228151786198097262922242993596257343257051703400175843430154722557677920874807863425475530765933204100503499768839606352399220179853720663569342290259555641027439
442943927504266724069376833160154122078614671268885319775025357850108512766756965068892272622194031924162199016275425966326165256651539551252483744445116646306879821859693369143742705388846172736661389828863605451



p29 by Sean A. Irvine







 1234567...199


Sm199 = p3 * p40 * c447 [ Length = 489 ]



151 * 
4386264746954920374371567783174533011041 * 
186398832942377429555452591563659684079765413854705864389921306888940333599059950208095535457614760128484399860037234160159192138094596242158068501774151388710210214383896282853147811799121298207590151664740033924177695648716063172173047017
911236453764993676049937409317754141571971633527089317399808119795275812472976282683848508770324255997254085144740663777094736682347251770666070758468752527785127982889419135231259082990979165068726974180289



p40 by Kevin Zhou

The following factor of Sm199 was found on 2024/05/25:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1:1648768524
Step 1 took 115453ms
********** Factor found in step 1: 4386264746954920374371567783174533011041
P = 2, Q = 3 (0.21%)

p40 submitted to factordb.com on May 26, 2024.







 1234567...200


Sm200 = (p1)^5 * p1 * (p1)^2 * c488 [ Length = 492 ]



2^5 * 
3 * 
5^2 * 
514403287921300547563173825800088426351052613678876305138931401557664183926810189436452062714688977315239941502567765194027820290446553072815699078325340951603577866204128830391456654082912917087925429600437942112950454625462967137975479650
487992163000504675513017188025529700538042213050554725563067238075579750588092263100604775613117288125629800638142313150654825663167338175679850688192363200704875713217388225729900738242413250754925763267438275779950788292463300804975813317
48832583




Source Smarandache Factors and Reverse Factors by Fleuren, Micha (page 18 of 35) dd. November 12, 1998.

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( © All rights reserved ) - Last modified : October 9, 2024.
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E-mail address : pdg@worldofnumbers.com