Smoothly Undulating Palindromic Primes

(95*10^5-59)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(95*10^5-59)/99
N=95959
*** N is prime!
Time: 0 sec

(95*10^17-59)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(95*10^17-59)/99
N=95959595959595959
Factor: 2 divides N - 1
Factor: 2^3 divides N + 1
Factor: 3 divides N - 1
Factor: 5 divides N + 1
Factor: 293 divides N + 1
Factor: 1009 divides N - 1
Factor: 1201 divides N + 1
Factorization results: F1=0.2227 F2=0.4209
F1=6054
F2=14075720
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=95959595959595957
Pass: 3^(N-1) = 1 (mod N): R20=1
Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=1 q=-3 R20=0
Pass: gcd(U{(N+1)/2}, N) = 1: d=13 p=3 q=-1 R20=47744011705221737
Pass: U{N+1} = 0 (mod N): d=13 p=3 q=-1 R20=0
Pass: gcd(3^((N-1)/3) - 1, N) = 1: R20=20847121376160149
Pass: gcd(U{(N+1)/5}, N) = 1: d=13 p=3 q=-1 R20=3523491833649059
Pass: gcd(U{(N+1)/293}, N) = 1: d=13 p=3 q=-1 R20=45872842779529860
Pass: gcd(3^((N-1)/1009) - 1, N) = 1: R20=51864658273670082
Pass: gcd(U{(N+1)/1201}, N) = 1: d=13 p=3 q=-1 R20=51141800105141034
BLS tests passed: F1=0.2227 F2=0.4209
Main divisor test: F1=0.2050 F2=0.4209 G=0.6259 S=0.0000 T=1
G=42607204440
Main divisor test passed: 1/1
*** N is prime!
Time: 0 sec

(95*10^209-59)/99


*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(95*10^209-59)/99
N=95959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959595959
Factor: 2 divides N - 1
Factor: 2^3 divides N + 1
Factor: 3 divides N - 1
Factor: 5 divides N + 1
Factor: 23 divides N - 1
Factor: 61 divides N + 1
Factor: 571 divides N + 1
Factorization results: F1=0.0102 F2=0.0294
F1=138
F2=1393240
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=59595959595959595957
Pass: 3^(N-1) = 1 (mod N): R20=1
Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=1 q=-3 R20=0
Pass: gcd(U{(N+1)/2}, N) = 1: d=13 p=3 q=-1 R20=70665275182922711761
Pass: U{N+1} = 0 (mod N): d=13 p=3 q=-1 R20=0
Pass: gcd(3^((N-1)/3) - 1, N) = 1: R20=16527840786781046381
Pass: gcd(U{(N+1)/5}, N) = 1: d=13 p=3 q=-1 R20=6113381471239359653
Pass: gcd(3^((N-1)/23) - 1, N) = 1: R20=22245841683351707190
Pass: gcd(U{(N+1)/61}, N) = 1: d=13 p=3 q=-1 R20=11627695011569103595
Pass: gcd(U{(N+1)/571}, N) = 1: d=13 p=3 q=-1 R20=78054053200673750925
BLS tests passed: F1=0.0102 F2=0.0294
APRCL test
T=166320
S=806451601478192474336202485589822862857362784366868177258651623875694560574081270955940775834613529
APRCL main test (1) at level 8 for p=2
APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=1 R20=59595959595959595958
APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=0 R20=45454545454545454545
APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=0 R20=1
APRCL L_2 condition satisfied
APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=3 R20=45627876397107166338
APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=0 R20=1
APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=0 R20=1
APRCL main test (1 8) for p=2 q=61 not needed
APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=1 R20=59595959595959595958
APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=3 R20=19881060421600962141
APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=0 R20=31327406724983111540
APRCL main test (1 12) done: p=2 q=29 k=2 g=2 h=1 R20=36877694903854237980
APRCL main test (1 13) done: p=2 q=43 k=1 g=3 h=1 R20=59595959595959595958
APRCL main test (1 14) done: p=2 q=71 k=1 g=7 h=0 R20=1
APRCL main test (1 15) done: p=2 q=127 k=1 g=3 h=0 R20=1
APRCL main test (1 16) done: p=2 q=211 k=1 g=2 h=1 R20=59595959595959595958
APRCL main test (1 17) done: p=2 q=421 k=2 g=2 h=0 R20=80091855756064375966
APRCL main test (1 18) done: p=2 q=631 k=1 g=3 h=0 R20=1
APRCL main test (1 19) done: p=2 q=41 k=3 g=6 h=2 R20=90742306524170836314
APRCL main test (1 20) done: p=2 q=73 k=3 g=5 h=0 R20=69257463784866518479
APRCL main test (1 21) done: p=2 q=281 k=3 g=3 h=1 R20=64814017777933812762
APRCL main test (1 22) done: p=2 q=2521 k=3 g=17 h=0 R20=51915528655418622906
APRCL main test (1 23) done: p=2 q=17 k=4 g=3 h=6 R20=22340201321530671105
APRCL main test (1 24) done: p=2 q=113 k=4 g=3 h=12 R20=71199101336931922945
APRCL main test (1 25) done: p=2 q=241 k=4 g=7 h=14 R20=95391821751008272513
APRCL main test (1 26) done: p=2 q=337 k=4 g=10 h=13 R20=94114129137677189735
APRCL main test (1 27) done: p=2 q=1009 k=4 g=11 h=5 R20=38832551862336738395
APRCL main test (1 28) done: p=2 q=109 k=2 g=6 h=3 R20=55125618613540505637
APRCL main test (1 29) done: p=2 q=271 k=1 g=6 h=0 R20=1
APRCL main test (1 30) done: p=2 q=379 k=1 g=2 h=1 R20=59595959595959595958
APRCL main test (1 31) done: p=2 q=433 k=4 g=5 h=14 R20=16942261152725241388
APRCL main test (1 32) done: p=2 q=541 k=2 g=2 h=2 R20=93358156442880083977
APRCL main test (1 33) done: p=2 q=757 k=2 g=2 h=1 R20=65978575245147562698
APRCL main test (1 34) done: p=2 q=2161 k=4 g=23 h=6 R20=81100558695454023657
APRCL main test (1 35) done: p=2 q=7561 k=3 g=13 h=6 R20=94079091966494021818
APRCL main test (1 36) done: p=2 q=15121 k=4 g=11 h=8 R20=65440495850538364223
APRCL main test (1 37) for p=2 q=23 not needed
APRCL main test (1 38) done: p=2 q=67 k=1 g=2 h=0 R20=1
APRCL main test (1 39) done: p=2 q=89 k=3 g=3 h=5 R20=77324339201501925547
APRCL main test (1 40) done: p=2 q=199 k=1 g=3 h=0 R20=1
APRCL main test (1 41) done: p=2 q=331 k=1 g=3 h=0 R20=1
APRCL main test (1 42) done: p=2 q=397 k=2 g=5 h=0 R20=1645832279869676211
APRCL main test (1 43) done: p=2 q=463 k=1 g=3 h=0 R20=1
APRCL main test (1 44) done: p=2 q=617 k=3 g=3 h=7 R20=68530308245448978846
APRCL main test (1 45) done: p=2 q=661 k=2 g=2 h=3 R20=80210725749164048078
APRCL main test (1 46) done: p=2 q=881 k=4 g=3 h=4 R20=82324646185569998734
APRCL main test (1 47) done: p=2 q=991 k=1 g=6 h=1 R20=59595959595959595958
APRCL tests for p=2 completed
APRCL main test (2) at level 8 for p=3
APRCL L_3 condition satisfied
APRCL main test (2 4) done: p=3 q=7 k=1 g=3 h=1 R20=1
APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=2 R20=59595959595959595956
APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=0 R20=2
APRCL main test (2 8) for p=3 q=61 not needed
APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=8 R20=12586482903191749743
APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=8 R20=35252927365916158297
APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=6 R20=24036764341489759751
APRCL main test (2 13) done: p=3 q=43 k=1 g=3 h=0 R20=2
APRCL main test (2 15) done: p=3 q=127 k=2 g=3 h=0 R20=40600686331590027138
APRCL main test (2 16) done: p=3 q=211 k=1 g=2 h=2 R20=59595959595959595956
APRCL main test (2 17) done: p=3 q=421 k=1 g=2 h=1 R20=1
APRCL main test (2 18) done: p=3 q=631 k=2 g=3 h=2 R20=39682755280396744963
APRCL main test (2 20) done: p=3 q=73 k=2 g=5 h=3 R20=38977190960135856830
APRCL main test (2 22) done: p=3 q=2521 k=2 g=17 h=0 R20=81197650454098526414
APRCL main test (2 25) done: p=3 q=241 k=1 g=7 h=2 R20=59595959595959595956
APRCL main test (2 26) done: p=3 q=337 k=1 g=10 h=1 R20=1
APRCL main test (2 27) done: p=3 q=1009 k=2 g=11 h=6 R20=51896837380584974419
APRCL main test (2 28) done: p=3 q=109 k=3 g=6 h=15 R20=59352659395437196436
APRCL main test (2 29) done: p=3 q=271 k=3 g=6 h=26 R20=77718330704999932868
APRCL main test (2 30) done: p=3 q=379 k=3 g=2 h=6 R20=92687289012716414782
APRCL main test (2 31) done: p=3 q=433 k=3 g=5 h=0 R20=68979572980031332452
APRCL main test (2 32) done: p=3 q=541 k=3 g=2 h=23 R20=24964085783386528735
APRCL main test (2 33) done: p=3 q=757 k=3 g=2 h=23 R20=39333626620238050399
APRCL main test (2 34) done: p=3 q=2161 k=3 g=23 h=10 R20=82591245260428586168
APRCL main test (2 35) done: p=3 q=7561 k=3 g=13 h=9 R20=53762264938701352513
APRCL main test (2 36) done: p=3 q=15121 k=3 g=11 h=5 R20=76558239490586471551
APRCL main test (2 38) done: p=3 q=67 k=1 g=2 h=2 R20=59595959595959595956
APRCL main test (2 40) done: p=3 q=199 k=2 g=3 h=1 R20=94670714634574206248
APRCL main test (2 41) done: p=3 q=331 k=1 g=3 h=1 R20=1
APRCL main test (2 42) done: p=3 q=397 k=2 g=5 h=1 R20=8967396893782036432
APRCL main test (2 43) done: p=3 q=463 k=1 g=3 h=1 R20=1
APRCL main test (2 45) done: p=3 q=661 k=1 g=2 h=0 R20=2
APRCL main test (2 47) done: p=3 q=991 k=2 g=6 h=5 R20=32247676278790361217
APRCL tests for p=3 completed
APRCL main test (3) at level 8 for p=5
APRCL L_5 condition satisfied
APRCL main test (3 6) done: p=5 q=11 k=1 g=2 h=2 R20=10212694404037518951
APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=1 R20=61217696951578826036
APRCL main test (3 8) for p=5 q=61 not needed
APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=0 R20=83105480871572366066
APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=4 R20=22757720541387125802
APRCL main test (3 16) done: p=5 q=211 k=1 g=2 h=4 R20=78194431943979731306
APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=0 R20=9740378215933579802
APRCL main test (3 18) done: p=5 q=631 k=1 g=3 h=0 R20=13940830987014542236
APRCL main test (3 19) done: p=5 q=41 k=1 g=6 h=4 R20=42874895859266544785
APRCL main test (3 21) done: p=5 q=281 k=1 g=3 h=4 R20=97419910147307710421
APRCL main test (3 22) done: p=5 q=2521 k=1 g=17 h=4 R20=70200594768000575086
APRCL main test (3 25) done: p=5 q=241 k=1 g=7 h=0 R20=31118028180707938300
APRCL main test (3 29) done: p=5 q=271 k=1 g=6 h=1 R20=20948252797575323628
APRCL main test (3 32) done: p=5 q=541 k=1 g=2 h=3 R20=14210192345298656039
APRCL main test (3 34) done: p=5 q=2161 k=1 g=23 h=2 R20=90524532220910848473
APRCL main test (3 35) done: p=5 q=7561 k=1 g=13 h=1 R20=71748990665050802968
APRCL main test (3 36) done: p=5 q=15121 k=1 g=11 h=4 R20=3729077750883052103
APRCL main test (3 41) done: p=5 q=331 k=1 g=3 h=2 R20=26906482298597894793
APRCL main test (3 45) done: p=5 q=661 k=1 g=2 h=1 R20=47454118886505594702
APRCL main test (3 46) done: p=5 q=881 k=1 g=3 h=0 R20=10590109777341886591
APRCL main test (3 47) done: p=5 q=991 k=1 g=6 h=0 R20=67456266988782483204
APRCL tests for p=5 completed
APRCL main test (4) at level 8 for p=7
APRCL L_7 condition satisfied
APRCL main test (4 12) done: p=7 q=29 k=1 g=2 h=4 R20=17108305735617642912
APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=2 R20=82389020041288761664
APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=2 R20=86735158500535351452
APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=3 R20=50552394675327179712
APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=5 R20=55673325954054117488
APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=5 R20=45926592277222315596
APRCL main test (4 18) done: p=7 q=631 k=1 g=3 h=4 R20=41740382521773033878
APRCL main test (4 21) done: p=7 q=281 k=1 g=3 h=4 R20=71138848207889696456
APRCL main test (4 22) done: p=7 q=2521 k=1 g=17 h=4 R20=68303917668800783959
APRCL main test (4 24) done: p=7 q=113 k=1 g=3 h=2 R20=71616722611093536911
APRCL main test (4 26) done: p=7 q=337 k=1 g=10 h=0 R20=8995219159623461217
APRCL main test (4 27) done: p=7 q=1009 k=1 g=11 h=6 R20=20132609232307467411
APRCL main test (4 30) done: p=7 q=379 k=1 g=2 h=1 R20=17213220017507101931
APRCL main test (4 33) done: p=7 q=757 k=1 g=2 h=1 R20=39783378690874442883
APRCL main test (4 35) done: p=7 q=7561 k=1 g=13 h=6 R20=21510422997978188454
APRCL main test (4 36) done: p=7 q=15121 k=1 g=11 h=3 R20=36033731582867422288
APRCL main test (4 43) done: p=7 q=463 k=1 g=3 h=1 R20=14113487416043500141
APRCL main test (4 44) done: p=7 q=617 k=1 g=3 h=6 R20=96857242762630064731
APRCL tests for p=7 completed
APRCL main test (5) at level 8 for p=11
APRCL main test (5 37) done: p=11 q=23 k=1 g=5 h=0 R20=87780149045375863979
APRCL L_11 condition satisfied
APRCL main test (5 38) done: p=11 q=67 k=1 g=2 h=4 R20=58737582970289860613
APRCL main test (5 39) done: p=11 q=89 k=1 g=3 h=4 R20=33948856805430113723
APRCL main test (5 40) done: p=11 q=199 k=1 g=3 h=9 R20=81782010259230314769
APRCL main test (5 41) done: p=11 q=331 k=1 g=3 h=5 R20=80367191126651635914
APRCL main test (5 42) done: p=11 q=397 k=1 g=5 h=1 R20=67640346155704250878
APRCL main test (5 43) done: p=11 q=463 k=1 g=3 h=6 R20=71557222990920645049
APRCL main test (5 44) done: p=11 q=617 k=1 g=3 h=5 R20=63447662550505104166
APRCL main test (5 45) done: p=11 q=661 k=1 g=2 h=2 R20=4094740974674398859
APRCL main test (5 46) done: p=11 q=881 k=1 g=3 h=6 R20=94582822723889567689
APRCL main test (5 47) done: p=11 q=991 k=1 g=6 h=6 R20=46968613728279646899
APRCL tests for p=11 completed
Main divisor test: F1=0.0088 F2=0.0294 G=0.5115 S=0.4733 T=166320
G=77527063417799904923147781820598371575870056672699383930585221402951515580622076306319189930143369766933240
Main divisor test passed: 166320/166320
*** N is prime!
Time: 48 sec

(95*10^1295-59)/99

== BPI:B263C000F8A34 ============================================

TITANIX 2.1.0 - Primality Certificate

Started 07.18.2001 at 12:16:58 AM
Running time 4h 56mn 55s

Candidate certified prime

=================================================================

Proved prime with Titanix by Hans Rosenthal.
The zipped file "959_647.zip" is 170 KB.
When unpacked the file "Titanix-B263C000F8A34-001.out" is 401 KB
and is available on demand by simple email request.

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Patrick De Geest - Belgium

- Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com