Legend
F_ba Decomposition of the basenumber in its prime factors.
F_po Decomposition of the palindromic octagonal.
Note : a palindromic octagonal will always be divisible by its basenumber.
To reconstruct the octagonal you must take into account the green together with
the purple prime factors.
Date Date of discovery by the author.
Hypertext links to related topics in number theory
Comm Comments about the palindromic octagonal number.
Factorization
[46]
F_ba 1505189034316273989876364558 =
2 * 138569 * 5431189639516320352591
F_po 6796782087077872316108073397933708016132787707802876976 =
2^3 * 59 * 9566879455400046545824351
Date June 16, 2023 ( Patrick De Geest / CUDA code from Robert Xiao )
[45]
F_ba 1050527056977712014268976327 =
PRIME
F_po 3310821292326758954662668504058662664598576232921280133 =
7 * 71 * 101 * 109 * 15061 * 49247039 * 776587337
Date June 16, 2023 ( Patrick De Geest / CUDA code from Robert Xiao )
[44]
F_ba 233009668152040466112406343 =
11 * 21182697104730951464764213
F_po 162880516356972063257851225522158752360279653615088261 =
59809 * 19705009 * 593132904343267
Date June 15, 2023 ( Patrick De Geest / CUDA code from Robert Xiao )
[43]
F_ba 134655235447046729292188665 =
5 * 23 * 61 * 227 * 1929966757 * 43814704049
F_po 54396097299898769932478624342687423996789899279069345 =
105632642813 * 3824250682208861
Date January 8, 2023 ( David Griffeath / CUDA code from Robert Xiao )
[42]
F_ba 10504193933024178843891507 =
3 * 139 * 223 * 112959253401126763277
F_po 331014270547745901058874464478850109547745072410133 =
17 * 37 * 73 * 686294439947569234307
Date December 6, 2022 ( Robert Xiao )
[41]
F_ba 1505231393963863016048058 =
2 * 3 * 3 * 3 * 487 * 571 * 100240780229128051
F_po 6797164648123182571630290920361752813218464617976 =
2 * 2 * 31 * 97 * 146213 * 2567704929536273
Date December 6, 2022 ( Robert Xiao )
[40]
F_ba 1498828240862001472469376 =
2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 11 * 41 * 43 * 22434253 * 8971478741
F_po 6739458286816445701381236321831075446186828549376 =
2 * 13 * 47 * 21107 * 98963 * 1761580742413
Date December 6, 2022 ( Robert Xiao )
[39]
F_ba 1057171651503698963468087 =
29 * 239 * 3517 * 4649 * 237977 * 39199697
F_po 3352835702229174992660413140662994719222075382533 =
59 * 73 * 32693 * 15828041 * 1423016549
Date December 6, 2022 ( Robert Xiao )
[38]
F_ba 516618664116856556011482 =
2 * 3 * 11 * 227 * 1607 * 32401 * 662256162793
F_po 800684532341656355118723327811553656143235486008 =
2 * 2 * 47 * 97 * 1289 * 64734643 * 1018525927
Date November 9, 2022 ( David Griffeath / Rust code from Robert Xiao )
[37]
F_ba 1061445921245492013317 =
1621 * 654809328343918577
F_po 3380002331186073700219120073706811332000833 =
19 * 167596724407182949471
Date July 17, 2022 ( Patrick De Geest )
[36]
F_ba 790350914396051463771 =
3 * 3 * 691 * 1967741 * 64584970949
F_po 1873963703660024006763676004200663073693781 =
11 * 19 * 8053 * 1408760706247043
Date January 3, 2008 ( Feng Yuan )
[35]
F_ba 736230589620506244343 =
367427 * 606649 * 3302975141
F_po 1626106443278874830658560384788723446016261 =
47 * 43037 * 1091931172959793
Date July 5, 2022 ( Patrick De Geest )
[34]
F_ba 332369949023486562727 =
7 * 11 * 66429521 * 64978533331
F_po 331409349041625168935539861526140943904133 =
23 * 4349 * 7802453 * 1277599109
Date July 31, 2022 ( Patrick De Geest )
[33]
F_ba 246919023530449916313 =
3 * 12301 * 6691028467345471
F_po 182907012543692638362263836296345210709281 =
7 * 11 * 13 * 47 * 1019 * 35393 * 436568413
Date July 30, 2022 ( Patrick De Geest )
[32]
F_ba 65621182548683007153 =
3 * 3 * 19 * 23 * 41 * 8598589 * 47327009
F_po 12918418797262737739193773726279781481921 =
45659 * 64157 * 67203959839
Date January 3, 2008 ( Feng Yuan )
[31]
F_ba 704687633763271761 =
3 * 271 * 1327 * 2333 * 4091 * 68437
F_po 1489753983536637090907366353893579841 =
13 * 14519929 * 11199794653
Date April 2, 2002 ( Feng Yuan )
[30]
F_ba 589588144333920233 =
3511 * 465433 * 360795191
F_po 1042842539817346669666437189352482401 =
764783 * 768869 * 3008011
Date April 2, 2002 ( Feng Yuan )
[29]
F_ba 221420450951946111 =
3 * 19 * 227 * 424861 * 40278209
F_po 147081048299289519915982992840180741 =
11 * 60387395714167121
Date April 2, 2002 ( Feng Yuan )
[28]
F_ba 145815635485061318 =
2 * 7 * 624667 * 16673527711
F_po 63786598655736820002863755689568736 =
2 * 2 * 2 * 2 * 167 * 743 * 97369 * 2262973
Date April 2, 2002 ( Feng Yuan )
[27]
F_ba 136626014502187505 =
5 * 89 * 307024751690309
F_po 56000003516255851015855261530000065 =
149 * 919 * 2993318120123
Date April 2, 2002 ( Feng Yuan )
[26]
F_ba 7897699388697563 =
97 * 809 * 2477 * 5261 * 7723
F_po 187120966902701565107209669021781 =
4031761 * 5876612767
Date April 2, 2002 ( Feng Yuan )
[25]
F_ba 4731413168091258 =
2 * 3 * 3 * 11 * 37 * 61 * 10587517103
F_po 67158811701562055026510711885176 =
2 * 2 * 3548559876068443
Date April 2, 2002 ( Feng Yuan )
[24]
F_ba 222032718762723 =
3 * 3 * 3 * 3 * 11 * 9521 * 26173193
F_po 147895584603498894306485598741 =
223 * 12517 * 238634437
Date April 2, 2002 ( Feng Yuan )
[23]
F_ba 105802560494387 =
59 * 1793263737193
F_po 33582545421505050512454528533 =
89 * 250643 * 14228917
Date April 2, 2002 ( Feng Yuan )
[22]
F_ba 78849864240621 =
3 * 886607 * 29644801
F_po 18651903272292929227230915681 =
59 * 349 * 11488008971
Date April 2, 2002 ( Feng Yuan )
[21]
F_ba 51722791547842 =
2 * 619 * 41779314659
F_po 8025741496504444056941475.208 =
2 * 2 * 11 * 35963 * 98060617
Date April 2, 2002 ( Feng Yuan )
[20]
F_ba 5847307263801 =
3 * 3 * 649700807089
F_po 102573006711888117600375201 =
7 * 2505988827343
Date April 2, 2002 ( Feng Yuan )
[19]
F_ba 1400295262095 =
3 * 3 * 3 * 5 * 17 * 67 * 9106723
F_po 5882480463134313640842885 =
61 * 68866980103
Date April 2, 2002 ( Feng Yuan )
[18]
F_ba 335038979077 =
11 * 1201 * 25360607
F_po 336753352502205253357633 =
431 * 2332057859
Date April 2, 2002 ( Feng Yuan )
[17]
F_ba 13175129925 =
3 * 3 * 3 * 3 * 5 * 5 * 29 * 157 * 1429
F_po 520752145595541257025 =
43 * 919195111
Date July 24, 2000 ( Patrick De Geest )
[16]
F_ba 1050553507 =
29 * 36225983
F_po 3310988011108890133 =
7 * 450237217
[15]
F_ba 42687015 =
3 * 5 * 7 * 19 * 21397
F_po 5466543663456645 =
11 * 421 * 27653
[14]
F_ba 2017631 =
7 * 11 * 26203
F_po 12212500521221 =
13 * 353 * 1319
[13]
F_ba 1472746 =
2 * 11 * 66943
F_po 6506939396056 =
2 * 2 * 1104559
[12]
F_ba 1054167 =
3 * 37 * 9497
F_po 3333802083333 =
3162499
[11]
F_ba 1054067 =
7 * 23 * 6547
F_po 3333169613333 =
67 * 109 * 433
[10]
F_ba 453486 =
2 * 3 * 11 * 6871
F_po 616947749616 =
2 * 2 * 2 * 170057
[9]
F_ba 426115 =
5 * 85223
F_po 544721127445 =
11 * 251 * 463
[8]
F_ba 7863 =
3 * 2621
F_po 185464581 =
103 * 229
[7]
F_ba 7341 =
3 * 2447
F_po 161656161 =
19 * 19 * 61
[6]
F_ba 6431 =
59 * 109
F_po 124060421 =
101 * 191
[5]
F_ba 6331 =
13 * 487
F_po 120232021 =
7 * 2713
[4]
F_ba 52 =
2 * 2 * 13
F_po 8008 =
2 * 7 * 11
[3]
F_ba 2 =
PRIME
F_po 8 =
2 * 2
[2]
F_ba 1 =
1
F_po 1 =
1
[1]
F_ba 0 =
0
F_po 0 =
0
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