Smoothly Undulating Palindromic Primes

(72*10^3-27)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(72*10^3-27)/99
N=727
*** N is prime!
Time: 0 sec

(72*10^5-27)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(72*10^5-27)/99
N=72727
*** N is prime!
Time: 0 sec

(72*10^9-27)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(72*10^9-27)/99
N=727272727
*** N is prime!
Time: 0 sec

(72*10^17-27)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(72*10^17-27)/99
N=72727272727272727
Factor: 2 divides N - 1
Factor: 2^3 divides N + 1
Factor: 3 divides N - 1
Factor: 103 divides N + 1
Factor: 4013 divides N + 1
Factorization results: F1=0.0461 F2=0.3866
F1=6
F2=3306712
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=72727272727272725
Pass: 3^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=18048139038493350
Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0
Fail: gcd(3^((N-1)/3) - 1, N) not = 1: R20=0
Pass: gcd(5^((N-1)/3) - 1, N) = 1: R20=28337584124749350
Pass: 5^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/103}, N) = 1: d=5 p=1 q=-1 R20=21078171723723010
Pass: gcd(U{(N+1)/4013}, N) = 1: d=5 p=1 q=-1 R20=18098783591779991
BLS tests passed: F1=0.0461 F2=0.3866
Main divisor test: F1=0.0283 F2=0.3866 G=0.4149 S=0.0000 T=1
G=9920136
Main divisor test passed: 1/1
Final divisor test: F=0.3866 G=0.4149 H=1.1882 t=1 a=1
Final divisor test passed: 5/5 r=5 i=0
*** N is prime!
Time: 0 sec

(72*10^71-27)/99
*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(7210^71-27)/99 N=72727272727272727272727272727272727272727272727272727272727272727272727 Factor: 2 divides N - 1 Factor: 2^3 divides N + 1 Factor: 3 divides N - 1 Factor: 23 divides N - 1 Factorization results: F1=0.0302 F2=0.0127 F1=138 F2=8 Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=27272727272727272725 Pass: 3^(N-1) = 1 (mod N): R20=1 Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=41147741733923783897 Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0 Pass: gcd(3^((N-1)/3) - 1, N) = 1: R20=17036236148326118056 Pass: gcd(3^((N-1)/23) - 1, N) = 1: R20=3221910912397990147 BLS tests passed: F1=0.0302 F2=0.0127 APRCL test T=2520 S=22342564747827993241663860420075425 APRCL main test (1) at level 5 for p=2 APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=1 R20=27272727272727272726 APRCL L_2 condition satisfied APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=3 R20=36363636363636363636 APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=1 R20=27272727272727272726 APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=3 R20=23184507799892415277 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) done: p=2 q=61 k=2 g=2 h=1 R20=18880555080501331509 APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=0 R20=1 APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=1 R20=72986254067335148416 APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=3 R20=23660338928493136240 APRCL main test (1 12) done: p=2 q=29 k=2 g=2 h=3 R20=79872446222030050805 APRCL main test (1 13) done: p=2 q=43 k=1 g=3 h=1 R20=27272727272727272726 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=0 R20=1 APRCL main test (1 17) done: p=2 q=421 k=2 g=2 h=1 R20=36324244698153669554 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=1 R20=27957471970082450392 APRCL main test (1 20) done: p=2 q=73 k=3 g=5 h=5 R20=91659175979263204155 APRCL main test (1 21) done: p=2 q=281 k=3 g=3 h=6 R20=72858499666848477157 APRCL tests for p=2 completed APRCL main test (2) at level 5 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=0 R20=2 APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=2 R20=27272727272727272724 APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=2 R20=27272727272727272724 APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=2 R20=11795870238261746136 APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=4 R20=94651463274547362264 APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=3 R20=34977751348754764305 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=5 R20=28887540473524968604 APRCL main test (2 16) done: p=3 q=211 k=1 g=2 h=0 R20=2 APRCL main test (2 17) done: p=3 q=421 k=1 g=2 h=0 R20=2 APRCL main test (2 18) done: p=3 q=631 k=2 g=3 h=2 R20=91026536098178865627 APRCL main test (2 20) done: p=3 q=73 k=2 g=5 h=8 R20=41075460503992322257 APRCL tests for p=3 completed APRCL main test (3) at level 5 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=52742299023290758828 APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=1 R20=30035001418976444991 APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=3 R20=59790867557596931421 APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=0 R20=31336594787038912676 APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=3 R20=27180754179365565995 APRCL main test (3 16) done: p=5 q=211 k=1 g=2 h=4 R20=47634517725036805920 APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=3 R20=43260511753129149781 APRCL main test (3 18) done: p=5 q=631 k=1 g=3 h=4 R20=44161030336974239064 APRCL main test (3 19) done: p=5 q=41 k=1 g=6 h=2 R20=48753447623168027689 APRCL main test (3 21) done: p=5 q=281 k=1 g=3 h=3 R20=98991907397322728942 APRCL tests for p=5 completed APRCL main test (4) at level 5 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=81641563710636238500 APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=1 R20=65378784532577723179 APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=5 R20=67512117347086533858 APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=6 R20=76698323753522318852 APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=0 R20=78851157219007811666 APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=1 R20=47995077257220597664 APRCL main test (4 18) done: p=7 q=631 k=1 g=3 h=2 R20=75351694492475985706 APRCL main test (4 21) done: p=7 q=281 k=1 g=3 h=1 R20=98126745821511556179 APRCL tests for p=7 completed Main divisor test: F1=0.0259 F2=0.0127 G=0.5234 S=0.4847 T=2520 G=12333095740801052269398450951881634600 Main divisor test passed: 2520/2520 N is prime**! Time: 1 sec

(72*10^71-27)/99


*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(72*10^71-27)/99
N=72727272727272727272727272727272727272727272727272727272727272727272727
Factor: 2 divides N - 1
Factor: 2^3 divides N + 1
Factor: 3 divides N - 1
Factor: 23 divides N - 1
Factorization results: F1=0.0302 F2=0.0127
F1=138
F2=8
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=27272727272727272725
Pass: 3^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=41147741733923783897
Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0
Pass: gcd(3^((N-1)/3) - 1, N) = 1: R20=17036236148326118056
Pass: gcd(3^((N-1)/23) - 1, N) = 1: R20=3221910912397990147
BLS tests passed: F1=0.0302 F2=0.0127
APRCL test
T=2520
S=22342564747827993241663860420075425
APRCL main test (1) at level 5 for p=2
APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=1 R20=27272727272727272726
APRCL L_2 condition satisfied
APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=3 R20=36363636363636363636
APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=1 R20=27272727272727272726
APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=3 R20=23184507799892415277
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) done: p=2 q=61 k=2 g=2 h=1 R20=18880555080501331509
APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=0 R20=1
APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=1 R20=72986254067335148416
APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=3 R20=23660338928493136240
APRCL main test (1 12) done: p=2 q=29 k=2 g=2 h=3 R20=79872446222030050805
APRCL main test (1 13) done: p=2 q=43 k=1 g=3 h=1 R20=27272727272727272726
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=0 R20=1
APRCL main test (1 17) done: p=2 q=421 k=2 g=2 h=1 R20=36324244698153669554
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=1 R20=27957471970082450392
APRCL main test (1 20) done: p=2 q=73 k=3 g=5 h=5 R20=91659175979263204155
APRCL main test (1 21) done: p=2 q=281 k=3 g=3 h=6 R20=72858499666848477157
APRCL tests for p=2 completed
APRCL main test (2) at level 5 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=0 R20=2
APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=2 R20=27272727272727272724
APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=2 R20=27272727272727272724
APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=2 R20=11795870238261746136
APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=4 R20=94651463274547362264
APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=3 R20=34977751348754764305
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=5 R20=28887540473524968604
APRCL main test (2 16) done: p=3 q=211 k=1 g=2 h=0 R20=2
APRCL main test (2 17) done: p=3 q=421 k=1 g=2 h=0 R20=2
APRCL main test (2 18) done: p=3 q=631 k=2 g=3 h=2 R20=91026536098178865627
APRCL main test (2 20) done: p=3 q=73 k=2 g=5 h=8 R20=41075460503992322257
APRCL tests for p=3 completed
APRCL main test (3) at level 5 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=52742299023290758828
APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=1 R20=30035001418976444991
APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=3 R20=59790867557596931421
APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=0 R20=31336594787038912676
APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=3 R20=27180754179365565995
APRCL main test (3 16) done: p=5 q=211 k=1 g=2 h=4 R20=47634517725036805920
APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=3 R20=43260511753129149781
APRCL main test (3 18) done: p=5 q=631 k=1 g=3 h=4 R20=44161030336974239064
APRCL main test (3 19) done: p=5 q=41 k=1 g=6 h=2 R20=48753447623168027689
APRCL main test (3 21) done: p=5 q=281 k=1 g=3 h=3 R20=98991907397322728942
APRCL tests for p=5 completed
APRCL main test (4) at level 5 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=81641563710636238500
APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=1 R20=65378784532577723179
APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=5 R20=67512117347086533858
APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=6 R20=76698323753522318852
APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=0 R20=78851157219007811666
APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=1 R20=47995077257220597664
APRCL main test (4 18) done: p=7 q=631 k=1 g=3 h=2 R20=75351694492475985706
APRCL main test (4 21) done: p=7 q=281 k=1 g=3 h=1 R20=98126745821511556179
APRCL tests for p=7 completed
Main divisor test: F1=0.0259 F2=0.0127 G=0.5234 S=0.4847 T=2520
G=12333095740801052269398450951881634600
Main divisor test passed: 2520/2520
*** N is prime!
Time: 1 sec

(72*10^99-27)/99
*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(7210^99-27)/99 N=727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727 Factor: 2 divides N - 1 Factor: 2^3 divides N + 1 Factor: 3 divides N - 1 Factor: 7 divides N + 1 Factor: 11 divides N + 1 Factor: 13 divides N + 1 Factor: 19 divides N + 1 Factor: 23 divides N + 1 Factor: 4093 divides N + 1 Factor: 8779 divides N + 1 Factor: 52579 divides N + 1 Factor: 75577 divides N - 1 Factorization results: F1=0.0572 F2=0.1904 F1=453462 F2=6611570254611570248 Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=27272727272727272725 Pass: 3^(N-1) = 1 (mod N): R20=1 Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=16737083883079803907 Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0 Fail: gcd(3^((N-1)/3) - 1, N) not = 1: R20=0 Fail: gcd(5^((N-1)/3) - 1, N) not = 1: R20=0 Fail: gcd(21^((N-1)/3) - 1, N) not = 1: R20=0 Fail: gcd(27^((N-1)/3) - 1, N) not = 1: R20=0 Fail: gcd(29^((N-1)/3) - 1, N) not = 1: R20=0 Pass: gcd(33^((N-1)/3) - 1, N) = 1: R20=42970804309956830782 Pass: 33^(N-1) = 1 (mod N): R20=1 Pass: gcd(U{(N+1)/7}, N) = 1: d=5 p=1 q=-1 R20=14366287589158093494 Pass: gcd(U{(N+1)/11}, N) = 1: d=5 p=1 q=-1 R20=31571180513053535740 Pass: gcd(U{(N+1)/13}, N) = 1: d=5 p=1 q=-1 R20=21326542554477074014 Pass: gcd(U{(N+1)/19}, N) = 1: d=5 p=1 q=-1 R20=92254318802545820037 Pass: gcd(U{(N+1)/23}, N) = 1: d=5 p=1 q=-1 R20=81526040349714935472 Pass: gcd(U{(N+1)/4093}, N) = 1: d=5 p=1 q=-1 R20=32242026527570439062 Pass: gcd(U{(N+1)/8779}, N) = 1: d=5 p=1 q=-1 R20=72358436288239264053 Pass: gcd(U{(N+1)/52579}, N) = 1: d=5 p=1 q=-1 R20=37903062512624294872 Pass: gcd(33^((N-1)/75577) - 1, N) = 1: R20=44698419769319024094 BLS tests passed: F1=0.0572 F2=0.1904 APRCL test T=2520 S=597229136096237084876535725 APRCL main test (1) at level 5 for p=2 APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=1 R20=27272727272727272726 APRCL L_2 condition satisfied APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=3 R20=36363636363636363636 APRCL main test (1 4) for p=2 q=7 not needed APRCL main test (1 5) for p=2 q=13 not needed APRCL main test (1 6) for p=2 q=11 not needed APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=0 R20=1 APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=2 R20=49214531772983802008 APRCL main test (1 9) for p=2 q=19 not needed APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=3 R20=85955242711999468756 APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=1 R20=59377696873499809918 APRCL main test (1 12) done: p=2 q=29 k=2 g=2 h=3 R20=75483731488487731056 APRCL main test (1 13) done: p=2 q=43 k=1 g=3 h=0 R20=1 APRCL main test (1 14) done: p=2 q=71 k=1 g=7 h=1 R20=27272727272727272726 APRCL main test (1 15) done: p=2 q=127 k=1 g=3 h=1 R20=27272727272727272726 APRCL main test (1 16) done: p=2 q=211 k=1 g=2 h=1 R20=27272727272727272726 APRCL main test (1 17) done: p=2 q=421 k=2 g=2 h=3 R20=3300744594801838893 APRCL main test (1 18) done: p=2 q=631 k=1 g=3 h=1 R20=27272727272727272726 APRCL main test (1 19) done: p=2 q=41 k=3 g=6 h=6 R20=42668989597328406388 APRCL main test (1 20) done: p=2 q=73 k=3 g=5 h=2 R20=12614013925045643813 APRCL tests for p=2 completed APRCL main test (2) at level 5 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) for p=3 q=13 not needed APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=1 R20=1 APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=1 R20=1 APRCL main test (2 9) for p=3 q=19 not needed APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=2 R20=88388711814088491637 APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=4 R20=78701605530731866554 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=2 R20=52190284034175586440 APRCL main test (2 16) done: p=3 q=211 k=1 g=2 h=1 R20=1 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=93941049054203565337 APRCL main test (2 20) done: p=3 q=73 k=2 g=5 h=6 R20=5376457199588768966 APRCL tests for p=3 completed APRCL main test (3) at level 5 for p=5 APRCL L_5 condition satisfied APRCL main test (3 6) for p=5 q=11 not needed APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=1 R20=79576199035096017406 APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=3 R20=28059417067748161540 APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=3 R20=61338453982146177134 APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=4 R20=33155398459901534688 APRCL main test (3 16) done: p=5 q=211 k=1 g=2 h=4 R20=94577635477435571773 APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=3 R20=73257675348049471418 APRCL main test (3 18) done: p=5 q=631 k=1 g=3 h=3 R20=92539153302764002958 APRCL main test (3 19) done: p=5 q=41 k=1 g=6 h=4 R20=78697744848845384241 APRCL tests for p=5 completed APRCL main test (4) at level 5 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=40453010491506440562 APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=5 R20=31317379234794664477 APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=4 R20=24994789130293572545 APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=6 R20=69890408256065534461 APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=3 R20=2024789269773937735 APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=2 R20=88330494994128692584 APRCL main test (4 18) done: p=7 q=631 k=1 g=3 h=5 R20=17115017113673955273 APRCL tests for p=7 completed Main divisor test: F1=0.0542 F2=0.1904 G=0.5154 S=0.2708 T=2520 G=895275103424795989033350180850185778410156484063800 Main divisor test passed: 1260/2520 N is prime**! Time: 1 sec

(72*10^99-27)/99


*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(72*10^99-27)/99
N=727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727
Factor: 2 divides N - 1
Factor: 2^3 divides N + 1
Factor: 3 divides N - 1
Factor: 7 divides N + 1
Factor: 11 divides N + 1
Factor: 13 divides N + 1
Factor: 19 divides N + 1
Factor: 23 divides N + 1
Factor: 4093 divides N + 1
Factor: 8779 divides N + 1
Factor: 52579 divides N + 1
Factor: 75577 divides N - 1
Factorization results: F1=0.0572 F2=0.1904
F1=453462
F2=6611570254611570248
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=27272727272727272725
Pass: 3^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=16737083883079803907
Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0
Fail: gcd(3^((N-1)/3) - 1, N) not = 1: R20=0
Fail: gcd(5^((N-1)/3) - 1, N) not = 1: R20=0
Fail: gcd(21^((N-1)/3) - 1, N) not = 1: R20=0
Fail: gcd(27^((N-1)/3) - 1, N) not = 1: R20=0
Fail: gcd(29^((N-1)/3) - 1, N) not = 1: R20=0
Pass: gcd(33^((N-1)/3) - 1, N) = 1: R20=42970804309956830782
Pass: 33^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/7}, N) = 1: d=5 p=1 q=-1 R20=14366287589158093494
Pass: gcd(U{(N+1)/11}, N) = 1: d=5 p=1 q=-1 R20=31571180513053535740
Pass: gcd(U{(N+1)/13}, N) = 1: d=5 p=1 q=-1 R20=21326542554477074014
Pass: gcd(U{(N+1)/19}, N) = 1: d=5 p=1 q=-1 R20=92254318802545820037
Pass: gcd(U{(N+1)/23}, N) = 1: d=5 p=1 q=-1 R20=81526040349714935472
Pass: gcd(U{(N+1)/4093}, N) = 1: d=5 p=1 q=-1 R20=32242026527570439062
Pass: gcd(U{(N+1)/8779}, N) = 1: d=5 p=1 q=-1 R20=72358436288239264053
Pass: gcd(U{(N+1)/52579}, N) = 1: d=5 p=1 q=-1 R20=37903062512624294872
Pass: gcd(33^((N-1)/75577) - 1, N) = 1: R20=44698419769319024094
BLS tests passed: F1=0.0572 F2=0.1904
APRCL test
T=2520
S=597229136096237084876535725
APRCL main test (1) at level 5 for p=2
APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=1 R20=27272727272727272726
APRCL L_2 condition satisfied
APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=3 R20=36363636363636363636
APRCL main test (1 4) for p=2 q=7 not needed
APRCL main test (1 5) for p=2 q=13 not needed
APRCL main test (1 6) for p=2 q=11 not needed
APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=0 R20=1
APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=2 R20=49214531772983802008
APRCL main test (1 9) for p=2 q=19 not needed
APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=3 R20=85955242711999468756
APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=1 R20=59377696873499809918
APRCL main test (1 12) done: p=2 q=29 k=2 g=2 h=3 R20=75483731488487731056
APRCL main test (1 13) done: p=2 q=43 k=1 g=3 h=0 R20=1
APRCL main test (1 14) done: p=2 q=71 k=1 g=7 h=1 R20=27272727272727272726
APRCL main test (1 15) done: p=2 q=127 k=1 g=3 h=1 R20=27272727272727272726
APRCL main test (1 16) done: p=2 q=211 k=1 g=2 h=1 R20=27272727272727272726
APRCL main test (1 17) done: p=2 q=421 k=2 g=2 h=3 R20=3300744594801838893
APRCL main test (1 18) done: p=2 q=631 k=1 g=3 h=1 R20=27272727272727272726
APRCL main test (1 19) done: p=2 q=41 k=3 g=6 h=6 R20=42668989597328406388
APRCL main test (1 20) done: p=2 q=73 k=3 g=5 h=2 R20=12614013925045643813
APRCL tests for p=2 completed
APRCL main test (2) at level 5 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) for p=3 q=13 not needed
APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=1 R20=1
APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=1 R20=1
APRCL main test (2 9) for p=3 q=19 not needed
APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=2 R20=88388711814088491637
APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=4 R20=78701605530731866554
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=2 R20=52190284034175586440
APRCL main test (2 16) done: p=3 q=211 k=1 g=2 h=1 R20=1
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=93941049054203565337
APRCL main test (2 20) done: p=3 q=73 k=2 g=5 h=6 R20=5376457199588768966
APRCL tests for p=3 completed
APRCL main test (3) at level 5 for p=5
APRCL L_5 condition satisfied
APRCL main test (3 6) for p=5 q=11 not needed
APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=1 R20=79576199035096017406
APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=3 R20=28059417067748161540
APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=3 R20=61338453982146177134
APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=4 R20=33155398459901534688
APRCL main test (3 16) done: p=5 q=211 k=1 g=2 h=4 R20=94577635477435571773
APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=3 R20=73257675348049471418
APRCL main test (3 18) done: p=5 q=631 k=1 g=3 h=3 R20=92539153302764002958
APRCL main test (3 19) done: p=5 q=41 k=1 g=6 h=4 R20=78697744848845384241
APRCL tests for p=5 completed
APRCL main test (4) at level 5 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=40453010491506440562
APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=5 R20=31317379234794664477
APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=4 R20=24994789130293572545
APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=6 R20=69890408256065534461
APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=3 R20=2024789269773937735
APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=2 R20=88330494994128692584
APRCL main test (4 18) done: p=7 q=631 k=1 g=3 h=5 R20=17115017113673955273
APRCL tests for p=7 completed
Main divisor test: F1=0.0542 F2=0.1904 G=0.5154 S=0.2708 T=2520
G=895275103424795989033350180850185778410156484063800
Main divisor test passed: 1260/2520
*** N is prime!
Time: 1 sec

(72*10^243-27)/99


*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(72*10^243-27)/99
N=7272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727\
272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272\
72727272727272727272727272727272727272727272727
Factor: 2 divides N - 1
Factor: 2^3 divides N + 1
Factor: 3 divides N - 1
Factor: 7 divides N + 1
Factor: 13 divides N + 1
Factor: 19 divides N + 1
Factor: 487^2 divides N + 1
Factor: 1459 divides N + 1
Factor: 24083 divides N - 1
Factor: 52579 divides N + 1
Factor: 69499 divides N + 1
Factorization results: F1=0.0212 F2=0.0916
F1=144498
F2=17489970311983788476312
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=27272727272727272725
Pass: 3^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=1 q=-1 R20=62674649719157603946
Pass: U{N+1} = 0 (mod N): d=5 p=1 q=-1 R20=0
Fail: gcd(3^((N-1)/3) - 1, N) not = 1: R20=0
Fail: gcd(5^((N-1)/3) - 1, N) not = 1: R20=0
Pass: gcd(21^((N-1)/3) - 1, N) = 1: R20=51101131434196084652
Pass: 21^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/7}, N) = 1: d=5 p=1 q=-1 R20=64675734280418955725
Pass: gcd(U{(N+1)/13}, N) = 1: d=5 p=1 q=-1 R20=26254447862005541459
Fail: gcd(U{(N+1)/19}, N) not = 1: d=5 p=1 q=-1 R20=0
Fail: gcd(U{(N+1)/19}, N) not = 1: d=5 p=3 q=1 R20=0
Fail: gcd(U{(N+1)/19}, N) not = 1: d=5 p=5 q=5 R20=0
Pass: gcd(U{(N+1)/19}, N) = 1: d=5 p=7 q=11 R20=42959439963937080734
Pass: U{N+1} = 0 (mod N): d=5 p=7 q=11 R20=0
Pass: gcd(U{(N+1)/487}, N) = 1: d=5 p=7 q=11 R20=73538219310216616770
Pass: gcd(U{(N+1)/1459}, N) = 1: d=5 p=7 q=11 R20=75423913521801033858
Pass: gcd(21^((N-1)/24083) - 1, N) = 1: R20=82010354092086475538
Pass: gcd(U{(N+1)/52579}, N) = 1: d=5 p=7 q=11 R20=88437275847555895008
Pass: gcd(U{(N+1)/69499}, N) = 1: d=5 p=7 q=11 R20=96674786706277576803
BLS tests passed: F1=0.0212 F2=0.0916
APRCL test
T=166320
S=2358355657986040358212118784174736714935952087474196740118824164855423734050634890981539191265475
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=27272727272727272726
APRCL L_2 condition satisfied
APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=3 R20=36363636363636363636
APRCL main test (1 4) for p=2 q=7 not needed
APRCL main test (1 5) for p=2 q=13 not needed
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=27272727272727272726
APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=2 R20=47885465783880188610
APRCL main test (1 9) for p=2 q=19 not needed
APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=3 R20=97748854505611262368
APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=1 R20=78786861317919588424
APRCL main test (1 12) done: p=2 q=29 k=2 g=2 h=1 R20=89276834936763593125
APRCL main test (1 13) done: p=2 q=43 k=1 g=3 h=1 R20=27272727272727272726
APRCL main test (1 14) done: p=2 q=71 k=1 g=7 h=1 R20=27272727272727272726
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=0 R20=1
APRCL main test (1 17) done: p=2 q=421 k=2 g=2 h=3 R20=83677078615608639700
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=1 R20=13569697687896200500
APRCL main test (1 20) done: p=2 q=73 k=3 g=5 h=2 R20=44885972403774010975
APRCL main test (1 21) done: p=2 q=281 k=3 g=3 h=5 R20=25057455373091745013
APRCL main test (1 22) done: p=2 q=2521 k=3 g=17 h=5 R20=85471100912763047838
APRCL main test (1 23) done: p=2 q=17 k=4 g=3 h=4 R20=7453028903615521949
APRCL main test (1 24) done: p=2 q=113 k=4 g=3 h=5 R20=85222116074930350490
APRCL main test (1 25) done: p=2 q=241 k=4 g=7 h=12 R20=87723792931993464391
APRCL main test (1 26) done: p=2 q=337 k=4 g=10 h=6 R20=99866372661966624570
APRCL main test (1 27) done: p=2 q=1009 k=4 g=11 h=4 R20=18598889717857208209
APRCL main test (1 28) done: p=2 q=109 k=2 g=6 h=1 R20=7749577247094291114
APRCL main test (1 29) done: p=2 q=271 k=1 g=6 h=1 R20=27272727272727272726
APRCL main test (1 30) done: p=2 q=379 k=1 g=2 h=1 R20=27272727272727272726
APRCL main test (1 31) done: p=2 q=433 k=4 g=5 h=5 R20=69817596714596817090
APRCL main test (1 32) done: p=2 q=541 k=2 g=2 h=2 R20=24228270866419567565
APRCL main test (1 33) done: p=2 q=757 k=2 g=2 h=1 R20=26866209600670353590
APRCL main test (1 34) done: p=2 q=2161 k=4 g=23 h=4 R20=72867706076058554354
APRCL main test (1 35) done: p=2 q=7561 k=3 g=13 h=1 R20=3194883535452750938
APRCL main test (1 36) done: p=2 q=15121 k=4 g=11 h=1 R20=49769845001636799818
APRCL main test (1 37) done: p=2 q=23 k=1 g=5 h=0 R20=1
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=3 R20=17821741714042168531
APRCL main test (1 40) done: p=2 q=199 k=1 g=3 h=1 R20=27272727272727272726
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=2 R20=49047325977577422609
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=5 R20=6453385035139459091
APRCL main test (1 45) done: p=2 q=661 k=2 g=2 h=3 R20=80238782505096094967
APRCL main test (1 46) done: p=2 q=881 k=4 g=3 h=13 R20=18300675687365972504
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) for p=3 q=7 not needed
APRCL main test (2 5) for p=3 q=13 not needed
APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=1 R20=1
APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=1 R20=1
APRCL main test (2 9) for p=3 q=19 not needed
APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=2 R20=7414185203280351055
APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=8 R20=9370818126864202489
APRCL main test (2 13) done: p=3 q=43 k=1 g=3 h=2 R20=27272727272727272724
APRCL main test (2 15) done: p=3 q=127 k=2 g=3 h=8 R20=75275964766336124465
APRCL main test (2 16) done: p=3 q=211 k=1 g=2 h=2 R20=27272727272727272724
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=7 R20=37699156280343335520
APRCL main test (2 20) done: p=3 q=73 k=2 g=5 h=6 R20=6317112080210059518
APRCL main test (2 22) done: p=3 q=2521 k=2 g=17 h=3 R20=54958758111906764217
APRCL main test (2 25) done: p=3 q=241 k=1 g=7 h=2 R20=27272727272727272724
APRCL main test (2 26) done: p=3 q=337 k=1 g=10 h=2 R20=27272727272727272724
APRCL main test (2 27) done: p=3 q=1009 k=2 g=11 h=2 R20=80462141995421331021
APRCL main test (2 28) done: p=3 q=109 k=3 g=6 h=10 R20=84197830590404478733
APRCL main test (2 29) done: p=3 q=271 k=3 g=6 h=21 R20=70176767233270369834
APRCL main test (2 30) done: p=3 q=379 k=3 g=2 h=9 R20=4811294537697238171
APRCL main test (2 31) done: p=3 q=433 k=3 g=5 h=19 R20=18097207129331058157
APRCL main test (2 32) done: p=3 q=541 k=3 g=2 h=2 R20=17615992494828344887
APRCL main test (2 33) done: p=3 q=757 k=3 g=2 h=11 R20=42471336112213594133
APRCL main test (2 34) done: p=3 q=2161 k=3 g=23 h=22 R20=75758664324717712294
APRCL main test (2 35) done: p=3 q=7561 k=3 g=13 h=21 R20=40967716914286165779
APRCL main test (2 36) done: p=3 q=15121 k=3 g=11 h=23 R20=49983448579749997563
APRCL main test (2 38) done: p=3 q=67 k=1 g=2 h=2 R20=27272727272727272724
APRCL main test (2 40) done: p=3 q=199 k=2 g=3 h=8 R20=487206652145300069
APRCL main test (2 41) done: p=3 q=331 k=1 g=3 h=2 R20=27272727272727272724
APRCL main test (2 42) done: p=3 q=397 k=2 g=5 h=1 R20=30547692338510863322
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=2 R20=27272727272727272724
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=1 R20=47407963936889556724
APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=1 R20=51707501655472519156
APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=1 R20=42708460580000488627
APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=2 R20=44637332082770256208
APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=2 R20=57412850985554814160
APRCL main test (3 16) done: p=5 q=211 k=1 g=2 h=0 R20=29698752988885735230
APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=3 R20=9152715024381286702
APRCL main test (3 18) done: p=5 q=631 k=1 g=3 h=4 R20=77454803002257423961
APRCL main test (3 19) done: p=5 q=41 k=1 g=6 h=4 R20=48531718133145854740
APRCL main test (3 21) done: p=5 q=281 k=1 g=3 h=0 R20=92630654258546509151
APRCL main test (3 22) done: p=5 q=2521 k=1 g=17 h=0 R20=53062398888534321150
APRCL main test (3 25) done: p=5 q=241 k=1 g=7 h=0 R20=97164774585962237690
APRCL main test (3 29) done: p=5 q=271 k=1 g=6 h=4 R20=33652245277903969915
APRCL main test (3 32) done: p=5 q=541 k=1 g=2 h=3 R20=39812318158367269857
APRCL main test (3 34) done: p=5 q=2161 k=1 g=23 h=2 R20=62272036488217018894
APRCL main test (3 35) done: p=5 q=7561 k=1 g=13 h=1 R20=18538897425140131182
APRCL main test (3 36) done: p=5 q=15121 k=1 g=11 h=2 R20=3242469729577992920
APRCL main test (3 41) done: p=5 q=331 k=1 g=3 h=1 R20=23331875725519449107
APRCL main test (3 45) done: p=5 q=661 k=1 g=2 h=3 R20=44660850900651688437
APRCL main test (3 46) done: p=5 q=881 k=1 g=3 h=2 R20=96982537948136580379
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=3 R20=49451800226562598958
APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=6 R20=61246710479662650762
APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=5 R20=67753325366938896493
APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=4 R20=95681071283757290498
APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=3 R20=16910949202269259512
APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=0 R20=18167802691238406595
APRCL main test (4 18) done: p=7 q=631 k=1 g=3 h=2 R20=86180316183205131614
APRCL main test (4 21) done: p=7 q=281 k=1 g=3 h=4 R20=76861123458603833667
APRCL main test (4 22) done: p=7 q=2521 k=1 g=17 h=5 R20=56739745053043694202
APRCL main test (4 24) done: p=7 q=113 k=1 g=3 h=2 R20=88292382239710814432
APRCL main test (4 26) done: p=7 q=337 k=1 g=10 h=3 R20=38910698634910253754
APRCL main test (4 27) done: p=7 q=1009 k=1 g=11 h=3 R20=85854883148882000124
APRCL main test (4 30) done: p=7 q=379 k=1 g=2 h=0 R20=84202888581202237122
APRCL main test (4 33) done: p=7 q=757 k=1 g=2 h=6 R20=15157039760461285381
APRCL main test (4 35) done: p=7 q=7561 k=1 g=13 h=0 R20=41590506807915851649
APRCL main test (4 36) done: p=7 q=15121 k=1 g=11 h=1 R20=99934021302255307670
APRCL main test (4 43) done: p=7 q=463 k=1 g=3 h=6 R20=72402810761316789878
APRCL main test (4 44) done: p=7 q=617 k=1 g=3 h=3 R20=12635578672660075725
APRCL tests for p=7 completed
APRCL main test (5) at level 8 for p=11
APRCL L_11 condition satisfied
APRCL main test (5 37) done: p=11 q=23 k=1 g=5 h=1 R20=32730150883343660196
APRCL main test (5 38) done: p=11 q=67 k=1 g=2 h=4 R20=57357337995508353122
APRCL main test (5 39) done: p=11 q=89 k=1 g=3 h=4 R20=31555567231024473081
APRCL main test (5 40) done: p=11 q=199 k=1 g=3 h=6 R20=61050776865415271274
APRCL main test (5 41) done: p=11 q=331 k=1 g=3 h=4 R20=33549199513705262891
APRCL main test (5 42) done: p=11 q=397 k=1 g=5 h=10 R20=82820509825487510729
APRCL main test (5 43) done: p=11 q=463 k=1 g=3 h=7 R20=80522255771861778706
APRCL main test (5 44) done: p=11 q=617 k=1 g=3 h=0 R20=68958652627092888075
APRCL main test (5 45) done: p=11 q=661 k=1 g=2 h=6 R20=24243415588139419446
APRCL main test (5 46) done: p=11 q=881 k=1 g=3 h=3 R20=72211306317948739601
APRCL tests for p=11 completed
Main divisor test: F1=0.0200 F2=0.0916 G=0.5084 S=0.3968 T=166320
G=2980095716956163845580574064542044564284764439838090802683521563272015883364189749772257516312293581883559222580492721521800
Main divisor test passed: 166320/166320
*** N is prime!
Time: 66 sec

(72*10^7595-27)/99

By Hans Rosenthal

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 and 251

(72*10^7595-27)/99 is 3-PRP! (12.630000 seconds)
(72*10^7595-27)/99 is 5-PRP! (12.630000 seconds)
(72*10^7595-27)/99 is 7-PRP! (12.580000 seconds)
(72*10^7595-27)/99 is 11-PRP! (12.580000 seconds)
(72*10^7595-27)/99 is 13-PRP! (12.580000 seconds)
(72*10^7595-27)/99 is 17-PRP! (12.580000 seconds)
(72*10^7595-27)/99 is 19-PRP! (12.580000 seconds)
(72*10^7595-27)/99 is 23-PRP! (12.580000 seconds)
(72*10^7595-27)/99 is 29-PRP! (12.580000 seconds)
(72*10^7595-27)/99 is 31-PRP! (12.570000 seconds)
(72*10^7595-27)/99 is 37-PRP! (12.630000 seconds)
(72*10^7595-27)/99 is 41-PRP! (12.580000 seconds)
(72*10^7595-27)/99 is 43-PRP! (12.580000 seconds)
(72*10^7595-27)/99 is 47-PRP! (12.640000 seconds)
(72*10^7595-27)/99 is 53-PRP! (12.580000 seconds)
(72*10^7595-27)/99 is 59-PRP! (12.630000 seconds)
(72*10^7595-27)/99 is 61-PRP! (12.580000 seconds)
(72*10^7595-27)/99 is 251-PRP! (12.580000 seconds)

(72*10^9273-27)/99

By Hans Rosenthal

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 and 251

(72*10^9273-27)/99 is 3-PRP! (18.450000 seconds)
(72*10^9273-27)/99 is 5-PRP! (18.450000 seconds)
(72*10^9273-27)/99 is 7-PRP! (18.460000 seconds)
(72*10^9273-27)/99 is 11-PRP! (18.400000 seconds)
(72*10^9273-27)/99 is 13-PRP! (18.460000 seconds)
(72*10^9273-27)/99 is 17-PRP! (18.460000 seconds)
(72*10^9273-27)/99 is 19-PRP! (18.450000 seconds)
(72*10^9273-27)/99 is 23-PRP! (18.400000 seconds)
(72*10^9273-27)/99 is 29-PRP! (18.400000 seconds)
(72*10^9273-27)/99 is 31-PRP! (18.450000 seconds)
(72*10^9273-27)/99 is 37-PRP! (18.450000 seconds)
(72*10^9273-27)/99 is 41-PRP! (18.450000 seconds)
(72*10^9273-27)/99 is 43-PRP! (18.460000 seconds)
(72*10^9273-27)/99 is 47-PRP! (18.400000 seconds)
(72*10^9273-27)/99 is 53-PRP! (18.460000 seconds)
(72*10^9273-27)/99 is 59-PRP! (18.450000 seconds)
(72*10^9273-27)/99 is 61-PRP! (18.450000 seconds)
(72*10^9273-27)/99 is 251-PRP! (18.450000 seconds)

(72*10^53847-27)/99

Tested by Patrick De Geest

PFGW test for probable primality in bases 3,5 and 7
using version 20040728.Win_Stable (v1.2 RC1) [FFT v23.8]

(72*10^53847-27)/99 is 3-PRP! (291.9488s+0.0044s)
(72*10^53847-27)/99 is 5-PRP! (297.4489s+0.0044s)
(72*10^53847-27)/99 is 7-PRP! (292.5152s+0.0044s)

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Patrick De Geest - Belgium

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