```

(91*10^3-19)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(91*10^3-19)/99
N=919
*** N is prime!
Time: 0 sec

(91*10^9-19)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(91*10^9-19)/99
N=919191919
*** N is prime!
Time: 0 sec

(91*10^11-19)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(91*10^11-19)/99
N=91919191919
Factor: 2 divides N - 1
Factor: 2^4 divides N + 1
Factor: 3 divides N + 1
Factor: 5 divides N + 1
Factor: 43 divides N - 1
Factor: 157 divides N + 1
Factorization results: F1=0.1765 F2=0.4174
F1=86
F2=37680
Pass: gcd(7^((N-1)/2) - 1, N) = 1: R20=91919191917
Pass: 7^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/2}, N) = 1: d=17 p=1 q=-4 R20=38429075813
Pass: U{N+1} = 0 (mod N): d=17 p=1 q=-4 R20=0
Fail: gcd(U{(N+1)/3}, N) not = 1: d=17 p=1 q=-4 R20=0
Pass: gcd(U{(N+1)/3}, N) = 1: d=17 p=3 q=-2 R20=90547883614
Pass: U{N+1} = 0 (mod N): d=17 p=3 q=-2 R20=0
Pass: gcd(U{(N+1)/5}, N) = 1: d=17 p=3 q=-2 R20=24328691414
Pass: gcd(7^((N-1)/43) - 1, N) = 1: R20=64649682890
Pass: gcd(U{(N+1)/157}, N) = 1: d=17 p=3 q=-2 R20=38536716605
BLS tests passed: F1=0.1765 F2=0.4174
Main divisor test: F1=0.1490 F2=0.4174 G=0.5664 S=0.0000 T=1
G=1620240
Main divisor test passed: 1/1
*** N is prime!
Time: 0 sec

(91*10^17-19)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(91*10^17-19)/99
N=91919191919191919
Factor: 2 divides N - 1
Factor: 2^4 divides N + 1
Factor: 3^2 divides N + 1
Factor: 5 divides N + 1
Factor: 29 divides N - 1
Factor: 79 divides N + 1
Factorization results: F1=0.1040 F2=0.2803
F1=58
F2=56880
Pass: gcd(7^((N-1)/2) - 1, N) = 1: R20=91919191919191917
Pass: 7^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/2}, N) = 1: d=21 p=1 q=-5 R20=35800430658758812
Pass: U{N+1} = 0 (mod N): d=21 p=1 q=-5 R20=0
Pass: gcd(U{(N+1)/3}, N) = 1: d=21 p=1 q=-5 R20=8999174815045168
Pass: gcd(U{(N+1)/5}, N) = 1: d=21 p=1 q=-5 R20=73943617370126866
Pass: gcd(7^((N-1)/29) - 1, N) = 1: R20=9453953799698218
Pass: gcd(U{(N+1)/79}, N) = 1: d=21 p=1 q=-5 R20=42016375063864109
BLS tests passed: F1=0.1040 F2=0.2803
Main divisor test: F1=0.0862 F2=0.2803 G=0.3665 S=0.0000 T=1
G=1649520
Main divisor test passed: 1/1
Final divisor test: F=0.2803 G=0.3665 H=0.9271 t=1 a=10
Final divisor test passed: 41/41 r=41 i=0
*** N is prime!
Time: 1 sec

(91*10^23-19)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(91*10^23-19)/99
N=91919191919191919191919
Factor: 2 divides N - 1
Factor: 2^4 divides N + 1
Factor: 3 divides N + 1
Factor: 5 divides N + 1
Factor: 109 divides N + 1
Factorization results: F1=0.0131 F2=0.1924
F1=2
F2=26160
Pass: gcd(U{(N+1)/2}, N) = 1: d=21 p=1 q=-5 R20=33335715281287678973
Pass: U{N+1} = 0 (mod N): d=21 p=1 q=-5 R20=0
Fail: gcd(U{(N+1)/3}, N) not = 1: d=21 p=1 q=-5 R20=0
Pass: gcd(U{(N+1)/3}, N) = 1: d=21 p=3 q=-3 R20=9058713874085846312
Pass: U{N+1} = 0 (mod N): d=21 p=3 q=-3 R20=0
Pass: gcd(U{(N+1)/5}, N) = 1: d=21 p=3 q=-3 R20=36524269491601210054
Pass: gcd(U{(N+1)/109}, N) = 1: d=21 p=3 q=-3 R20=10141956808215736120
BLS tests passed: F1=0.0131 F2=0.1924
APRCL test
T=180
S=35964929
APRCL main test (1) at level 3 for p=2
APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=0 R20=1
APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=0 R20=42424242424242424242
APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=1 R20=19191919191919191918
APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=2 R20=29137529137529137529
APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=19191919191919191918
APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=1 R20=19191919191919191918
APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=2 R20=92607341895167748433
APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=1 R20=19191919191919191918
Retry
APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=0 R20=8992038721768451498
Retry
APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=2 R20=65283092516693444626
Retry from the beginning
APRCL main test (1) at level 4 for p=2
APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=0 R20=1
APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=0 R20=42424242424242424242
APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=1 R20=19191919191919191918
APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=2 R20=29137529137529137529
APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=19191919191919191918
APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=1 R20=19191919191919191918
APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=2 R20=92607341895167748433
Retry
APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=1 R20=19191919191919191918
Retry
APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=0 R20=8992038721768451498
Retry
APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=2 R20=65283092516693444626
Retry
APRCL L_2 condition satisfied
APRCL main test (1 12) done: p=2 q=29 k=2 g=2 h=3 R20=98337717243781453056
APRCL tests for p=2 completed
APRCL main test (2) at level 4 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=93939393939393939395
APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=1 R20=77777777777777777778
APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=1 R20=54056695992179863147
APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=0 R20=40519953634707733068
APRCL main test (2 9) for p=3 q=19 not needed
APRCL main test (2 10) for p=3 q=37 not needed
APRCL main test (2 11) for p=3 q=181 not needed
APRCL tests for p=3 completed
APRCL main test (3) at level 4 for p=5
APRCL L_5 condition satisfied
APRCL main test (3 6) done: p=5 q=11 k=1 g=2 h=1 R20=42384873503587451343
APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=1 R20=30364556734427080914
APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=1 R20=61770489649216293083
APRCL main test (3 11) for p=5 q=181 not needed
APRCL tests for p=5 completed
APRCL main test (4) at level 4 for p=7
APRCL L_7 condition satisfied
APRCL main test (4 12) for p=7 q=29 not needed
APRCL tests for p=7 completed
Main divisor test: F1=0.0000 F2=0.1924 G=0.5025 S=0.3102 T=1260
G=346626199920
Main divisor test passed: 105/1260
*** N is prime!
Time: 0 sec

(91*10^25229-19)/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

(91*10^25229-19)/99 is 3-PRP! (215.090000 seconds)
(91*10^25229-19)/99 is 5-PRP! (218.990000 seconds)
(91*10^25229-19)/99 is 7-PRP! (210.580000 seconds)
(91*10^25229-19)/99 is 11-PRP! (211.630000 seconds)
(91*10^25229-19)/99 is 13-PRP! (209.700000 seconds)
(91*10^25229-19)/99 is 17-PRP! (215.370000 seconds)
(91*10^25229-19)/99 is 19-PRP! (206.140000 seconds)
(91*10^25229-19)/99 is 23-PRP! (213.770000 seconds)
(91*10^25229-19)/99 is 29-PRP! (217.010000 seconds)
(91*10^25229-19)/99 is 31-PRP! (207.680000 seconds)
(91*10^25229-19)/99 is 37-PRP! (211.460000 seconds)
(91*10^25229-19)/99 is 41-PRP! (220.090000 seconds)
(91*10^25229-19)/99 is 43-PRP! (217.340000 seconds)
(91*10^25229-19)/99 is 47-PRP! (210.140000 seconds)
(91*10^25229-19)/99 is 53-PRP! (219.430000 seconds)
(91*10^25229-19)/99 is 59-PRP! (207.560000 seconds)
(91*10^25229-19)/99 is 61-PRP! (210.530000 seconds)
(91*10^25229-19)/99 is 67-PRP! (207.010000 seconds)
(91*10^25229-19)/99 is 71-PRP! (208.170000 seconds)
(91*10^25229-19)/99 is 73-PRP! (209.810000 seconds)
(91*10^25229-19)/99 is 79-PRP! (209.930000 seconds)
(91*10^25229-19)/99 is 83-PRP! (214.810000 seconds)
(91*10^25229-19)/99 is 89-PRP! (207.060000 seconds)
(91*10^25229-19)/99 is 97-PRP! (213.280000 seconds)
(91*10^25229-19)/99 is 101-PRP! (209.770000 seconds)
(91*10^25229-19)/99 is 103-PRP! (205.420000 seconds)
(91*10^25229-19)/99 is 107-PRP! (212.890000 seconds)
(91*10^25229-19)/99 is 109-PRP! (216.950000 seconds)
(91*10^25229-19)/99 is 113-PRP! (208.500000 seconds)
(91*10^25229-19)/99 is 127-PRP! (214.210000 seconds)
(91*10^25229-19)/99 is 251-PRP! (215.860000 seconds)

```