```

(17*10^31-71)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(17*10^31-71)/99
N=1717171717171717171717171717171
Factor: 2 divides N - 1
Factor: 2^2 divides N + 1
Factor: 3 divides N - 1
Factor: 5 divides N - 1
Factor: 7 divides N - 1
Factor: 11 divides N + 1
Factor: 13 divides N - 1
Factor: 17 divides N - 1
Factor: 23 divides N + 1
Factor: 31 divides N - 1
Factor: 37 divides N - 1
Factor: 41 divides N - 1
Factorization results: F1=0.3089 F2=0.0994
F1=2182523070
F2=1012
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=71717171717171717169
Pass: 3^(N-1) = 1 (mod N): R20=1
Fail: gcd(U{(N+1)/2}, N) not = 1: d=29 p=1 q=-7 R20=0
Pass: gcd(U{(N+1)/2}, N) = 1: d=29 p=3 q=-5 R20=74368468112633149632
Pass: U{N+1} = 0 (mod N): d=29 p=3 q=-5 R20=0
Pass: gcd(3^((N-1)/3) - 1, N) = 1: R20=24873081318416479731
Pass: gcd(3^((N-1)/5) - 1, N) = 1: R20=36145982538848188424
Pass: gcd(3^((N-1)/7) - 1, N) = 1: R20=34733506295431959533
Pass: gcd(U{(N+1)/11}, N) = 1: d=29 p=3 q=-5 R20=75889137708777222826
Fail: gcd(3^((N-1)/13) - 1, N) not = 1: R20=0
Pass: gcd(7^((N-1)/13) - 1, N) = 1: R20=82754993074923534708
Pass: 7^(N-1) = 1 (mod N): R20=1
Pass: gcd(7^((N-1)/17) - 1, N) = 1: R20=56145531162052704949
Pass: gcd(U{(N+1)/23}, N) = 1: d=29 p=3 q=-5 R20=9893756714395431819
Pass: gcd(7^((N-1)/31) - 1, N) = 1: R20=89358476954355236642
Pass: gcd(7^((N-1)/37) - 1, N) = 1: R20=29054232281828764225
Pass: gcd(7^((N-1)/41) - 1, N) = 1: R20=6531438961362544188
BLS tests passed: F1=0.3089 F2=0.0994
Main divisor test: F1=0.2989 F2=0.0994 G=0.3983 S=0.0000 T=1
G=1104356673420
Main divisor test passed: 1/1
Final divisor test: F=0.3089 G=0.3983 H=1.0161 t=-1 a=1
Final divisor test passed: 3/3 r=3 i=0
*** N is prime!
Time: 0 sec

(17*10^37-71)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(17*10^37-71)/99
N=1717171717171717171717171717171717171
Factor: 2 divides N - 1
Factor: 2^2 divides N + 1
Factor: 3^2 divides N - 1
Factor: 5 divides N - 1
Factor: 7 divides N - 1
Factor: 13 divides N - 1
Factor: 17 divides N - 1
Factor: 19 divides N - 1
Factor: 37 divides N - 1
Factor: 101 divides N - 1
Factor: 9901 divides N - 1
Factorization results: F1=0.3861 F2=0.0166
F1=97878787878690
F2=4
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=71717171717171717169
Pass: 3^(N-1) = 1 (mod N): R20=1
Pass: gcd(3^((N-1)/3) - 1, N) = 1: R20=48601905774926808122
Pass: gcd(3^((N-1)/5) - 1, N) = 1: R20=35763837691649457780
Pass: gcd(3^((N-1)/7) - 1, N) = 1: R20=98408220656761682163
Pass: gcd(3^((N-1)/13) - 1, N) = 1: R20=41466020188593064714
Fail: gcd(3^((N-1)/17) - 1, N) not = 1: R20=0
Pass: gcd(7^((N-1)/17) - 1, N) = 1: R20=7153162019986157859
Pass: 7^(N-1) = 1 (mod N): R20=1
Pass: gcd(7^((N-1)/19) - 1, N) = 1: R20=82239478772342386392
Pass: gcd(7^((N-1)/37) - 1, N) = 1: R20=10975655667755510326
Pass: gcd(7^((N-1)/101) - 1, N) = 1: R20=64639804137182958668
Pass: gcd(7^((N-1)/9901) - 1, N) = 1: R20=74570143588062121701
BLS tests passed: F1=0.3861 F2=0.0166
Main divisor test: F1=0.3778 F2=0.0166 G=0.3944 S=0.0000 T=1
G=195757575757380
Main divisor test passed: 1/1
Final divisor test: F=0.3861 G=0.3944 H=1.1666 t=-1 a=1
Final divisor test passed: 3/3 r=3 i=0
*** N is prime!
Time: 0 sec

(17*10^4885-71)/99

== ID:B27B6046426BC =============================================

PRIMO 1.2.2 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 171717171717171717171717171717171717171717171717171717171717\
...
...
[= 1(71)_2442 = (17*10^4885-71)/99]

Decimal size = 4885
Binary size = 16226

-----------------------------------------------------------------
1) EC Test
-----------------------------------------------------------------
N = Candidate
S = 266269524
R = 644899833588059132038397198310880358849168077219275448029558\
...
...
...
-----------------------------------------------------------------
761) SPP Test
-----------------------------------------------------------------
N = R of preceding test

Started 07.31.2002 08:27:52 PM
Running time 2008h 56mn 53s

Candidate certified prime

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

Proved prime with 'Primo 1.2.2' by Hans Rosenthal.
The proof was done using Marcel Martin's Primo and took
2008 hours and 57 minutes on a AMD Athlon 1.33 GHz. The Primo
certificate was then validated with Cert_Val which took
on the same PC an additional 25 hours and 11 minutes.
The Primo certificate of the above record SUPP (the zipped file
of which is > 2.5 MB) is available on demand by simple email
request to Hans.

Here are the first and last lines from the Cert_Val output file:

+------------------------------------------------------------------------+
| Cert_Val a "PRIMO/Titanix" certificate (.out file) validation program  |
|    Version 1.95 Jim Fougeron, Using the Miracl big integer library     |
|  Copyright, 2001-2002 Jim Fougeron, Free usage rights granted to all   |
+------------------------------------------------------------------------+

Processing file primo-b27b6046426bc.out

This Certificate is a PRIMO compatible certificate

1) EC  Test ECtest1 != Ident, ECtest2= Ident	Validated 8mn 1.379s
2) EC  Test ECtest1 != Ident, ECtest2= Ident	Validated 7mn 57.941s
...
...
761) SPP Test Trial-div to 170101  !Success!!!	Validated 0.001s

Prime number being certified was:
N = 17171717171717171717171717171717171717171717171717\
...
17171717171717171717171717171717171

Certificate for this number was FULLY validated!
Total time used to validate certificate: 1 days 1h 10mn 59.059s
There were 761 steps in the primality proof

```