```

(74*10^5-47)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(74*10^5-47)/99
N=74747
*** N is prime!
Time: 0 sec

(74*10^17-47)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(74*10^17-47)/99
N=74747474747474747
Factor: 2 divides N - 1
Factor: 2^2 divides N + 1
Factor: 3 divides N + 1
Factor: 7 divides N - 1
Factor: 31 divides N - 1
Factor: 6263 divides N + 1
Factorization results: F1=0.1563 F2=0.2890
F1=434
F2=75156
Pass: gcd(5^((N-1)/2) - 1, N) = 1: R20=74747474747474745
Pass: 5^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=13469830502801851
Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0
Pass: gcd(U{(N+1)/3}, N) = 1: d=5 p=1 q=-1 R20=49036341709696196
Pass: gcd(5^((N-1)/7) - 1, N) = 1: R20=67394972705436510
Pass: gcd(5^((N-1)/31) - 1, N) = 1: R20=11122960336461072
Pass: gcd(U{(N+1)/6263}, N) = 1: d=5 p=1 q=-1 R20=46735292010519393
BLS tests passed: F1=0.1563 F2=0.2890
Main divisor test: F1=0.1385 F2=0.2890 G=0.4274 S=0.0000 T=1
G=16308852
Main divisor test passed: 1/1
Final divisor test: F=0.2890 G=0.4274 H=1.0054 t=1 a=1
Final divisor test passed: 5/5 r=5 i=0
*** N is prime!
Time: 0 sec

(74*10^2069-47)/99

== BPI:B263F011CA63C ============================================

TITANIX 2.1.0 - Primality Certificate

Started 07.21.2001 at 05:10:54 AM
Running time 53h 37mn 47s

Candidate certified prime

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

Proved prime with Titanix by Hans Rosenthal.
The zipped file "747_1034.zip" is 431 KB.
When unpacked the file "Titanix-B263F011CA63C-001.out" is 996 KB
and is available on demand by simple email request.

(74*10^6815-47)/99

PFGW 1.1 test for probable primality in basis
3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,
and 251

(74*10^6815-47)/99 is 3-PRP! (11.260000 seconds)
(74*10^6815-47)/99 is 5-PRP! (11.310000 seconds)
(74*10^6815-47)/99 is 7-PRP! (11.260000 seconds)
(74*10^6815-47)/99 is 11-PRP! (11.310000 seconds)
(74*10^6815-47)/99 is 13-PRP! (11.320000 seconds)
(74*10^6815-47)/99 is 17-PRP! (11.310000 seconds)
(74*10^6815-47)/99 is 19-PRP! (11.310000 seconds)
(74*10^6815-47)/99 is 23-PRP! (11.260000 seconds)
(74*10^6815-47)/99 is 29-PRP! (11.310000 seconds)
(74*10^6815-47)/99 is 31-PRP! (11.320000 seconds)
(74*10^6815-47)/99 is 37-PRP! (11.310000 seconds)
(74*10^6815-47)/99 is 41-PRP! (11.310000 seconds)
(74*10^6815-47)/99 is 43-PRP! (11.310000 seconds)
(74*10^6815-47)/99 is 47-PRP! (11.260000 seconds)
(74*10^6815-47)/99 is 53-PRP! (11.310000 seconds)
(74*10^6815-47)/99 is 59-PRP! (11.310000 seconds)
(74*10^6815-47)/99 is 61-PRP! (11.310000 seconds)
(74*10^6815-47)/99 is 251-PRP! (11.310000 seconds)

(74*10^20417-47)/99

PFGW 1.1 test for probable primality in bases
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67,
71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, and 251

(74*10^20417-47)/99 is 3-PRP! (148.300000 seconds)
(74*10^20417-47)/99 is 5-PRP! (147.700000 seconds)
(74*10^20417-47)/99 is 7-PRP! (149.670000 seconds)
(74*10^20417-47)/99 is 11-PRP! (147.090000 seconds)
(74*10^20417-47)/99 is 13-PRP! (142.480000 seconds)
(74*10^20417-47)/99 is 17-PRP! (152.420000 seconds)
(74*10^20417-47)/99 is 19-PRP! (148.410000 seconds)
(74*10^20417-47)/99 is 23-PRP! (144.780000 seconds)
(74*10^20417-47)/99 is 29-PRP! (142.040000 seconds)
(74*10^20417-47)/99 is 31-PRP! (154.780000 seconds)
(74*10^20417-47)/99 is 37-PRP! (152.750000 seconds)
(74*10^20417-47)/99 is 41-PRP! (153.580000 seconds)
(74*10^20417-47)/99 is 43-PRP! (146.870000 seconds)
(74*10^20417-47)/99 is 47-PRP! (146.590000 seconds)
(74*10^20417-47)/99 is 53-PRP! (158.510000 seconds)
(74*10^20417-47)/99 is 59-PRP! (146.710000 seconds)
(74*10^20417-47)/99 is 61-PRP! (144.230000 seconds)
(74*10^20417-47)/99 is 67-PRP! (149.340000 seconds)
(74*10^20417-47)/99 is 71-PRP! (146.100000 seconds)
(74*10^20417-47)/99 is 73-PRP! (146.930000 seconds)
(74*10^20417-47)/99 is 79-PRP! (148.740000 seconds)
(74*10^20417-47)/99 is 83-PRP! (148.190000 seconds)
(74*10^20417-47)/99 is 89-PRP! (149.070000 seconds)
(74*10^20417-47)/99 is 97-PRP! (159.840000 seconds)
(74*10^20417-47)/99 is 101-PRP! (153.790000 seconds)
(74*10^20417-47)/99 is 103-PRP! (153.130000 seconds)
(74*10^20417-47)/99 is 107-PRP! (141.550000 seconds)
(74*10^20417-47)/99 is 109-PRP! (149.010000 seconds)
(74*10^20417-47)/99 is 113-PRP! (146.650000 seconds)
(74*10^20417-47)/99 is 127-PRP! (153.350000 seconds)
(74*10^20417-47)/99 is 251-PRP! (142.480000 seconds)

(74*10^25745-47)/99

PFGW 1.1 test for probable primality in bases
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67,
71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, and 251

(74*10^25745-47)/99 is 3-PRP! (220.970000 seconds)
(74*10^25745-47)/99 is 5-PRP! (222.660000 seconds)
(74*10^25745-47)/99 is 7-PRP! (214.700000 seconds)
(74*10^25745-47)/99 is 11-PRP! (215.690000 seconds)
(74*10^25745-47)/99 is 13-PRP! (212.230000 seconds)
(74*10^25745-47)/99 is 17-PRP! (219.320000 seconds)
(74*10^25745-47)/99 is 19-PRP! (215.030000 seconds)
(74*10^25745-47)/99 is 23-PRP! (211.630000 seconds)
(74*10^25745-47)/99 is 29-PRP! (210.970000 seconds)
(74*10^25745-47)/99 is 31-PRP! (223.500000 seconds)
(74*10^25745-47)/99 is 37-PRP! (213.830000 seconds)
(74*10^25745-47)/99 is 41-PRP! (216.350000 seconds)
(74*10^25745-47)/99 is 43-PRP! (210.750000 seconds)
(74*10^25745-47)/99 is 47-PRP! (212.230000 seconds)
(74*10^25745-47)/99 is 53-PRP! (218.600000 seconds)
(74*10^25745-47)/99 is 59-PRP! (211.680000 seconds)
(74*10^25745-47)/99 is 61-PRP! (219.700000 seconds)
(74*10^25745-47)/99 is 67-PRP! (210.810000 seconds)
(74*10^25745-47)/99 is 71-PRP! (218.440000 seconds)
(74*10^25745-47)/99 is 73-PRP! (213.220000 seconds)
(74*10^25745-47)/99 is 79-PRP! (214.150000 seconds)
(74*10^25745-47)/99 is 83-PRP! (218.880000 seconds)
(74*10^25745-47)/99 is 89-PRP! (219.430000 seconds)
(74*10^25745-47)/99 is 97-PRP! (219.530000 seconds)
(74*10^25745-47)/99 is 101-PRP! (217.620000 seconds)
(74*10^25745-47)/99 is 103-PRP! (220.420000 seconds)
(74*10^25745-47)/99 is 107-PRP! (223.820000 seconds)
(74*10^25745-47)/99 is 109-PRP! (226.510000 seconds)
(74*10^25745-47)/99 is 113-PRP! (219.320000 seconds)
(74*10^25745-47)/99 is 127-PRP! (211.300000 seconds)
(74*10^25745-47)/99 is 251-PRP! (220.850000 seconds)

```