*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(94*10^5-49)/99 N=94949 *** N is prime! Time: 0 sec
*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(94*10^17-49)/99
N=94949494949494949
Factor: 2^2 divides N - 1
Factor: 2 divides N + 1
Factor: 3 divides N + 1
Factor: 5^2 divides N + 1
Factor: 7^2 divides N - 1
Factor: 8647 divides N + 1
Factorization results: F1=0.1350 F2=0.3601
F1=196
F2=1297050
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=94949494949494947
Pass: 3^(N-1) = 1 (mod N): R20=1
Fail: gcd(U{(N+1)/2}, N) not = 1: d=21 p=1 q=-5 R20=0
Pass: gcd(U{(N+1)/2}, N) = 1: d=21 p=3 q=-3 R20=15164378622157200
Pass: U{N+1} = 0 (mod N): d=21 p=3 q=-3 R20=0
Pass: gcd(U{(N+1)/3}, N) = 1: d=21 p=3 q=-3 R20=80994161678135484
Fail: gcd(U{(N+1)/5}, N) not = 1: d=21 p=3 q=-3 R20=0
Fail: gcd(U{(N+1)/5}, N) not = 1: d=21 p=5 q=1 R20=0
Fail: gcd(U{(N+1)/5}, N) not = 1: d=21 p=7 q=7 R20=0
Pass: gcd(U{(N+1)/5}, N) = 1: d=21 p=9 q=15 R20=50877680642346872
Pass: U{N+1} = 0 (mod N): d=21 p=9 q=15 R20=0
Fail: gcd(3^((N-1)/7) - 1, N) not = 1: R20=0
Pass: gcd(15^((N-1)/7) - 1, N) = 1: R20=52627428529815306
Pass: 15^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/8647}, N) = 1: d=21 p=9 q=15 R20=49689115071392752
BLS tests passed: F1=0.1350 F2=0.3601
Main divisor test: F1=0.1350 F2=0.3423 G=0.4773 S=0.0000 T=1
G=127110900
Main divisor test passed: 1/1
Final divisor test: F=0.3601 G=0.4773 H=1.1975 t=1 a=1
Final divisor test passed: 5/5 r=5 i=0
*** N is prime!
Time: 0 sec
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*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(94*10^65-49)/99
N=94949494949494949494949494949494949494949494949494949494949494949
Factor: 2^2 divides N - 1
Factor: 2 divides N + 1
Factor: 3 divides N + 1
Factor: 5^2 divides N + 1
Factor: 7 divides N - 1
Factor: 211 divides N + 1
Factor: 307 divides N - 1
Factor: 49463 divides N - 1
Factorization results: F1=0.1328 F2=0.0693
F1=425183948
F2=31650
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=49494949494949494947
Pass: 3^(N-1) = 1 (mod N): R20=1
Fail: gcd(U{(N+1)/2}, N) not = 1: d=21 p=1 q=-5 R20=0
Pass: gcd(U{(N+1)/2}, N) = 1: d=21 p=3 q=-3 R20=30858083144371414869
Pass: U{N+1} = 0 (mod N): d=21 p=3 q=-3 R20=0
Pass: gcd(U{(N+1)/3}, N) = 1: d=21 p=3 q=-3 R20=2950441950894746347
Pass: gcd(U{(N+1)/5}, N) = 1: d=21 p=3 q=-3 R20=30311041278775111995
Pass: gcd(3^((N-1)/7) - 1, N) = 1: R20=56019342171706509467
Pass: gcd(U{(N+1)/211}, N) = 1: d=21 p=3 q=-3 R20=94799673423714805221
Pass: gcd(3^((N-1)/307) - 1, N) = 1: R20=68150530396561506457
Pass: gcd(3^((N-1)/49463) - 1, N) = 1: R20=88610273254095866031
BLS tests passed: F1=0.1328 F2=0.0693
APRCL test
T=1260
S=162881621902321411661
APRCL main test (1) at level 4 for p=2
APRCL L_2 condition satisfied
APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=1 R20=49494949494949494948
APRCL main test (1 3) for p=2 q=5 not needed
APRCL main test (1 4) for p=2 q=7 not needed
APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=2 R20=49494949494949494947
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=1 R20=49494949494949494948
APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=3 R20=0
APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=1 R20=49494949494949494948
APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=0 R20=2
APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=3 R20=0
APRCL main test (1 12) done: p=2 q=29 k=2 g=2 h=2 R20=49494949494949494947
APRCL main test (1 13) done: p=2 q=43 k=1 g=3 h=1 R20=49494949494949494948
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) for p=2 q=211 not needed
APRCL main test (1 17) done: p=2 q=421 k=2 g=2 h=1 R20=0
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) for p=3 q=7 not needed
APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=2 R20=7614607614607614608
APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=0 R20=3160638644509612252
APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=0 R20=72793508859082629574
APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=6 R20=71245771610256229005
APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=4 R20=26021073866216305953
APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=3 R20=64481068457043124402
APRCL main test (2 13) done: p=3 q=43 k=1 g=3 h=1 R20=92600422832980972515
APRCL main test (2 15) done: p=3 q=127 k=2 g=3 h=4 R20=1011965501223613598
APRCL main test (2 16) for p=3 q=211 not needed
APRCL main test (2 17) done: p=3 q=421 k=1 g=2 h=2 R20=81086398426065884498
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=2 R20=20330325126321425630
APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=3 R20=1776691551456440572
APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=1 R20=36617017566003985967
APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=3 R20=4456585745805444199
APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=1 R20=71290245264087018754
APRCL main test (3 16) for p=5 q=211 not needed
APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=1 R20=28851310480670517190
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) done: p=7 q=29 k=1 g=2 h=6 R20=49494949494949494938
APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=1 R20=1
APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=4 R20=1
APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=5 R20=1
APRCL main test (4 16) for p=7 q=211 not needed
APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=1 R20=1
APRCL tests for p=7 completed
Main divisor test: F1=0.1328 F2=0.0646 G=0.5085 S=0.3111 T=1260
G=1095954852978168960368697968963100
Main divisor test passed: 1260/1260
*** N is prime!
Time: 0 sec
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*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(94*10^143-49)/99
|
*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(94*10^551-49)/99
|
Test by Ray Chandler PFGW Version 3.4.8.64BIT.20110617.Win_Dev [GWNUM 26.6] Primality testing (94*10^92981-49)/99 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Generic modular reduction using generic reduction Core2 type-1 FFT length 40K, Pass1=32, Pass2=1280 on A 308883-bit number Running N+1 test using discriminant 11, base 1+sqrt(11) Generic modular reduction using generic reduction Core2 type-1 FFT length 40K, Pass1=32, Pass2=1280 on A 308883-bit number Calling N+1 BLS with factored part 0.01% and helper 0.00% (0.03% proof) (94*10^92981-49)/99 is Fermat and Lucas PRP! (2801.8213s+0.0026s)
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