Smoothly Undulating Palindromic Primes

(73*10^15-37)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(73*10^15-37)/99
N=737373737373737
Factor: 2^3 divides N - 1
Factor: 2 divides N + 1
Factor: 3 divides N + 1
Factor: 19 divides N + 1
Factor: 43 divides N - 1
Factor: 8039 divides N + 1
Factorization results: F1=0.1706 F2=0.4010
F1=344
F2=916446
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=737373737373735
Pass: 3^(N-1) = 1 (mod N): R20=1
Fail: gcd(U{(N+1)/2}, N) not = 1: d=5 p=1 q=-1 R20=0
Fail: gcd(U{(N+1)/2}, N) not = 1: d=5 p=3 q=1 R20=0
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=5 q=5 R20=2
Pass: U{N+1} = 0 (mod N): d=5 p=5 q=5 R20=0
Fail: gcd(U{(N+1)/3}, N) not = 1: d=5 p=5 q=5 R20=0
Pass: gcd(U{(N+1)/3}, N) = 1: d=5 p=7 q=11 R20=61488000633561
Pass: U{N+1} = 0 (mod N): d=5 p=7 q=11 R20=0
Pass: gcd(U{(N+1)/19}, N) = 1: d=5 p=7 q=11 R20=104934067444636
Pass: gcd(3^((N-1)/43) - 1, N) = 1: R20=357766776001560
Pass: gcd(U{(N+1)/8039}, N) = 1: d=5 p=7 q=11 R20=669414354279174
BLS tests passed: F1=0.1706 F2=0.4010
Main divisor test: F1=0.1706 F2=0.3808 G=0.5514 S=0.0000 T=1
G=157628712
Main divisor test passed: 1/1
*** N is prime!
Time: 0 sec

(73*10^39-37)/99
*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(7310^39-37)/99 N=737373737373737373737373737373737373737 Factor: 2^3 divides N - 1 Factor: 2 divides N + 1 Factor: 3^3 divides N + 1 Factor: 29129 divides N - 1 Factorization results: F1=0.1381 F2=0.0446 F1=233032 F2=54 Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=37373737373737373735 Pass: 3^(N-1) = 1 (mod N): R20=1 Fail: gcd(U{(N+1)/2}, N) not = 1: d=5 p=1 q=-1 R20=0 Fail: gcd(U{(N+1)/2}, N) not = 1: d=5 p=3 q=1 R20=0 Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=5 q=5 R20=2 Pass: U{N+1} = 0 (mod N): d=5 p=5 q=5 R20=0 Pass: gcd(U{(N+1)/3}, N) = 1: d=5 p=5 q=5 R20=99050682978128807219 Pass: gcd(3^((N-1)/29129) - 1, N) = 1: R20=70705161453447288417 BLS tests passed: F1=0.1381 F2=0.0446 APRCL test T=180 S=6021428237825 APRCL main test (1) at level 3 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=37373737373737373736 APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=3 R20=0 APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=0 R20=1 APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=0 R20=2 APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=37373737373737373736 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=3 R20=0 APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=1 R20=37373737373737373736 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=0 R20=2 APRCL tests for p=2 completed APRCL main test (2) at level 3 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=16017316017316017317 APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=1 R20=23931623931623931624 APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=1 R20=32942326490713587487 APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=2 R20=85957940056300712038 APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=1 R20=77699179942734435930 APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=4 R20=53954131547121626636 APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=4 R20=77185129459906673925 APRCL tests for p=3 completed APRCL main test (3) at level 3 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=24526254278320394023 APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=3 R20=25822218017847570397 APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=0 R20=72468028850721675231 APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=4 R20=81260207459041438468 APRCL tests for p=5 completed Main divisor test: F1=0.1381 F2=0.0368 G=0.5037 S=0.3288 T=180 G=37886007558154555800 Main divisor test passed: 180/180 ** N is prime! Time: 0 sec

(73*10^39-37)/99


*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(73*10^39-37)/99
N=737373737373737373737373737373737373737
Factor: 2^3 divides N - 1
Factor: 2 divides N + 1
Factor: 3^3 divides N + 1
Factor: 29129 divides N - 1
Factorization results: F1=0.1381 F2=0.0446
F1=233032
F2=54
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=37373737373737373735
Pass: 3^(N-1) = 1 (mod N): R20=1
Fail: gcd(U{(N+1)/2}, N) not = 1: d=5 p=1 q=-1 R20=0
Fail: gcd(U{(N+1)/2}, N) not = 1: d=5 p=3 q=1 R20=0
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=5 q=5 R20=2
Pass: U{N+1} = 0 (mod N): d=5 p=5 q=5 R20=0
Pass: gcd(U{(N+1)/3}, N) = 1: d=5 p=5 q=5 R20=99050682978128807219
Pass: gcd(3^((N-1)/29129) - 1, N) = 1: R20=70705161453447288417
BLS tests passed: F1=0.1381 F2=0.0446
APRCL test
T=180
S=6021428237825
APRCL main test (1) at level 3 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=37373737373737373736
APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=3 R20=0
APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=0 R20=1
APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=0 R20=2
APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=37373737373737373736
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=3 R20=0
APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=1 R20=37373737373737373736
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=0 R20=2
APRCL tests for p=2 completed
APRCL main test (2) at level 3 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=16017316017316017317
APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=1 R20=23931623931623931624
APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=1 R20=32942326490713587487
APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=2 R20=85957940056300712038
APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=1 R20=77699179942734435930
APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=4 R20=53954131547121626636
APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=4 R20=77185129459906673925
APRCL tests for p=3 completed
APRCL main test (3) at level 3 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=24526254278320394023
APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=3 R20=25822218017847570397
APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=0 R20=72468028850721675231
APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=4 R20=81260207459041438468
APRCL tests for p=5 completed
Main divisor test: F1=0.1381 F2=0.0368 G=0.5037 S=0.3288 T=180
G=37886007558154555800
Main divisor test passed: 180/180
*** N is prime!
Time: 0 sec

(73*10^567-37)/99


*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(73*10^567-37)/99
N=737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737373737
Factor: 2^3 divides N - 1
Factor: 2 divides N + 1
Factor: 3 divides N + 1
Factor: 19 divides N - 1
Factor: 317 divides N - 1
Factor: 17257 divides N - 1
Factorization results: F1=0.0157 F2=0.0014
F1=831511288
F2=6
Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=37373737373737373735
Pass: 3^(N-1) = 1 (mod N): R20=1
Fail: gcd(U{(N+1)/2}, N) not = 1: d=5 p=1 q=-1 R20=0
Fail: gcd(U{(N+1)/2}, N) not = 1: d=5 p=3 q=1 R20=0
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=5 q=5 R20=2
Pass: U{N+1} = 0 (mod N): d=5 p=5 q=5 R20=0
Fail: gcd(U{(N+1)/3}, N) not = 1: d=5 p=5 q=5 R20=0
Pass: gcd(U{(N+1)/3}, N) = 1: d=5 p=7 q=11 R20=55836545579934906332
Pass: U{N+1} = 0 (mod N): d=5 p=7 q=11 R20=0
Pass: gcd(3^((N-1)/19) - 1, N) = 1: R20=64264836004943956982
Pass: gcd(3^((N-1)/317) - 1, N) = 1: R20=36835063511352247585
Pass: gcd(3^((N-1)/17257) - 1, N) = 1: R20=43331320253818186771
BLS tests passed: F1=0.0157 F2=0.0014
APRCL test
T=21621600
S=1055669171049266262396115679910539762370060186812284758794597107239945552236818627675628664769043776598396663026322926541549036674504870132007775163227252075616083544589237758581563159986793035726557636420050534049182651710425968378980368754786078398156774610007460528924432625
APRCL main test (1) at level 11 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=37373737373737373736
APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=3 R20=0
APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=0 R20=1
APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=0 R20=2
APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=37373737373737373736
APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=1 R20=37373737373737373736
APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=0 R20=2
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=0 R20=2
APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=1 R20=0
APRCL main test (1 12) done: p=2 q=29 k=2 g=2 h=0 R20=2
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=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=1 R20=37373737373737373736
APRCL main test (1 17) done: p=2 q=421 k=2 g=2 h=2 R20=37373737373737373735
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=0 R20=4
APRCL main test (1 20) done: p=2 q=73 k=3 g=5 h=5 R20=0
APRCL main test (1 21) done: p=2 q=281 k=3 g=3 h=0 R20=4
APRCL main test (1 22) done: p=2 q=2521 k=3 g=17 h=2 R20=0
APRCL main test (1 23) done: p=2 q=17 k=4 g=3 h=12 R20=26371258984162089487
APRCL main test (1 24) done: p=2 q=113 k=4 g=3 h=3 R20=4327998673623835089
APRCL main test (1 25) done: p=2 q=241 k=4 g=7 h=3 R20=60961425529214275547
APRCL main test (1 26) done: p=2 q=337 k=4 g=10 h=13 R20=33015902413370988943
APRCL main test (1 27) done: p=2 q=1009 k=4 g=11 h=9 R20=66273836841647292251
APRCL main test (1 28) done: p=2 q=109 k=2 g=6 h=1 R20=0
APRCL main test (1 29) done: p=2 q=271 k=1 g=6 h=0 R20=1
APRCL main test (1 30) done: p=2 q=379 k=1 g=2 h=0 R20=1
APRCL main test (1 31) done: p=2 q=433 k=4 g=5 h=7 R20=61852471287649528485
APRCL main test (1 32) done: p=2 q=541 k=2 g=2 h=0 R20=2
APRCL main test (1 33) done: p=2 q=757 k=2 g=2 h=2 R20=37373737373737373735
APRCL main test (1 34) done: p=2 q=2161 k=4 g=23 h=1 R20=49301686399863759446
APRCL main test (1 35) done: p=2 q=7561 k=3 g=13 h=1 R20=0
APRCL main test (1 36) done: p=2 q=15121 k=4 g=11 h=13 R20=1743741943509029436
APRCL main test (1 37) done: p=2 q=23 k=1 g=5 h=1 R20=37373737373737373736
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=7 R20=0
APRCL main test (1 40) done: p=2 q=199 k=1 g=3 h=1 R20=37373737373737373736
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=37373737373737373735
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=1 R20=0
APRCL main test (1 45) done: p=2 q=661 k=2 g=2 h=3 R20=0
APRCL main test (1 46) done: p=2 q=881 k=4 g=3 h=10 R20=25046741644812746187
APRCL main test (1 47) done: p=2 q=991 k=1 g=6 h=1 R20=37373737373737373736
APRCL main test (1 48) done: p=2 q=1321 k=3 g=13 h=5 R20=0
APRCL main test (1 49) done: p=2 q=2311 k=1 g=3 h=1 R20=37373737373737373736
APRCL main test (1 50) done: p=2 q=2377 k=3 g=5 h=0 R20=4
APRCL main test (1 51) done: p=2 q=2971 k=1 g=10 h=1 R20=37373737373737373736
APRCL main test (1 52) done: p=2 q=3697 k=4 g=5 h=14 R20=40094912004372722248
APRCL main test (1 53) done: p=2 q=4159 k=1 g=3 h=0 R20=1
APRCL main test (1 54) done: p=2 q=4621 k=2 g=2 h=3 R20=0
APRCL main test (1 55) done: p=2 q=8317 k=2 g=6 h=1 R20=0
APRCL main test (1 56) done: p=2 q=9241 k=3 g=13 h=5 R20=0
APRCL main test (1 57) done: p=2 q=16633 k=3 g=15 h=0 R20=4
APRCL main test (1 58) done: p=2 q=18481 k=4 g=13 h=15 R20=83046259059917313436
APRCL main test (1 59) done: p=2 q=23761 k=4 g=7 h=8 R20=63213023233480552639
APRCL main test (1 60) done: p=2 q=101 k=2 g=2 h=2 R20=37373737373737373735
APRCL main test (1 61) done: p=2 q=151 k=1 g=6 h=1 R20=37373737373737373736
APRCL main test (1 62) done: p=2 q=401 k=4 g=3 h=0 R20=40338669351418965963
APRCL main test (1 63) done: p=2 q=601 k=3 g=7 h=2 R20=0
APRCL main test (1 64) done: p=2 q=701 k=2 g=2 h=3 R20=0
APRCL main test (1 65) done: p=2 q=1051 k=1 g=7 h=1 R20=37373737373737373736
APRCL main test (1 66) done: p=2 q=1201 k=4 g=11 h=12 R20=92417816579750737025
APRCL main test (1 67) done: p=2 q=1801 k=3 g=11 h=7 R20=0
APRCL main test (1 68) done: p=2 q=2801 k=4 g=3 h=5 R20=170469923972451870
APRCL main test (1 69) done: p=2 q=3301 k=2 g=6 h=2 R20=37373737373737373735
APRCL main test (1 70) done: p=2 q=3851 k=1 g=2 h=0 R20=1
APRCL main test (1 71) done: p=2 q=4201 k=3 g=11 h=3 R20=0
APRCL main test (1 72) done: p=2 q=4951 k=1 g=6 h=0 R20=1
APRCL main test (1 73) done: p=2 q=6301 k=2 g=10 h=2 R20=37373737373737373735
APRCL main test (1 74) done: p=2 q=9901 k=2 g=2 h=3 R20=0
APRCL main test (1 75) done: p=2 q=11551 k=1 g=7 h=1 R20=37373737373737373736
APRCL main test (1 76) done: p=2 q=12601 k=3 g=11 h=2 R20=0
APRCL main test (1 77) done: p=2 q=14851 k=1 g=2 h=1 R20=37373737373737373736
APRCL main test (1 78) done: p=2 q=15401 k=3 g=6 h=5 R20=0
APRCL main test (1 79) done: p=2 q=19801 k=3 g=13 h=0 R20=4
APRCL main test (1 80) done: p=2 q=97 k=5 g=5 h=24 R20=8314304636072728102
APRCL main test (1 81) done: p=2 q=353 k=5 g=3 h=7 R20=21982289944202511478
APRCL main test (1 82) done: p=2 q=673 k=5 g=5 h=15 R20=21327377159207131089
APRCL main test (1 83) done: p=2 q=2017 k=5 g=5 h=9 R20=64435795239569726751
APRCL main test (1 84) done: p=2 q=3169 k=5 g=7 h=27 R20=17660153742207525736
APRCL main test (1 85) done: p=2 q=3361 k=5 g=22 h=26 R20=67922251774106442797
APRCL main test (1 86) done: p=2 q=5281 k=5 g=7 h=17 R20=82407928832991912386
APRCL main test (1 87) done: p=2 q=7393 k=5 g=5 h=6 R20=39402516206410654624
APRCL main test (1 88) done: p=2 q=21601 k=5 g=7 h=23 R20=23067726229577816420
APRCL main test (1 89) done: p=2 q=30241 k=5 g=11 h=25 R20=21124954323022005763
APRCL main test (1 90) done: p=2 q=53 k=2 g=2 h=3 R20=0
APRCL main test (1 91) done: p=2 q=79 k=1 g=3 h=0 R20=1
APRCL main test (1 92) done: p=2 q=131 k=1 g=2 h=0 R20=1
APRCL main test (1 93) done: p=2 q=157 k=2 g=5 h=2 R20=37373737373737373735
APRCL main test (1 94) done: p=2 q=313 k=3 g=10 h=3 R20=0
APRCL main test (1 95) done: p=2 q=521 k=3 g=3 h=5 R20=0
APRCL main test (1 96) done: p=2 q=547 k=1 g=2 h=1 R20=37373737373737373736
APRCL main test (1 97) done: p=2 q=859 k=1 g=2 h=1 R20=37373737373737373736
APRCL main test (1 98) done: p=2 q=911 k=1 g=17 h=0 R20=1
APRCL main test (1 99) done: p=2 q=937 k=3 g=5 h=6 R20=0
APRCL tests for p=2 completed
APRCL main test (2) at level 11 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=16017316017316017317
APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=1 R20=23931623931623931624
APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=0 R20=98370804822417725644
APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=2 R20=34608378870673952641
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=1 R20=92499272630755464941
APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=5 R20=72018094121572165554
APRCL main test (2 13) done: p=3 q=43 k=1 g=3 h=0 R20=48743246417665022316
APRCL main test (2 15) done: p=3 q=127 k=2 g=3 h=5 R20=41007564000334395324
APRCL main test (2 16) done: p=3 q=211 k=1 g=2 h=1 R20=13030781751160898080
APRCL main test (2 17) done: p=3 q=421 k=1 g=2 h=0 R20=50241128625926725689
APRCL main test (2 18) done: p=3 q=631 k=2 g=3 h=2 R20=35160082595051950658
APRCL main test (2 20) done: p=3 q=73 k=2 g=5 h=3 R20=15092186644072551372
APRCL main test (2 22) done: p=3 q=2521 k=2 g=17 h=7 R20=7994084045226040589
APRCL main test (2 25) done: p=3 q=241 k=1 g=7 h=1 R20=48480657194350140408
APRCL main test (2 26) done: p=3 q=337 k=1 g=10 h=0 R20=49836645385606809939
APRCL main test (2 27) done: p=3 q=1009 k=2 g=11 h=5 R20=12611979397602773260
APRCL main test (2 28) done: p=3 q=109 k=3 g=6 h=9 R20=22589224023947191624
APRCL main test (2 29) done: p=3 q=271 k=3 g=6 h=21 R20=32632313958661101303
APRCL main test (2 30) done: p=3 q=379 k=3 g=2 h=21 R20=53854352685432903989
APRCL main test (2 31) done: p=3 q=433 k=3 g=5 h=14 R20=37022869923774489321
APRCL main test (2 32) done: p=3 q=541 k=3 g=2 h=20 R20=67751717490376152422
APRCL main test (2 33) done: p=3 q=757 k=3 g=2 h=9 R20=28982144786133846219
APRCL main test (2 34) done: p=3 q=2161 k=3 g=23 h=25 R20=30018429744380901980
APRCL main test (2 35) done: p=3 q=7561 k=3 g=13 h=19 R20=63608564719085802649
APRCL main test (2 36) done: p=3 q=15121 k=3 g=11 h=8 R20=72326015096619637266
APRCL main test (2 38) done: p=3 q=67 k=1 g=2 h=0 R20=2382029247700889492
APRCL main test (2 40) done: p=3 q=199 k=2 g=3 h=7 R20=50689371467956953654
APRCL main test (2 41) done: p=3 q=331 k=1 g=3 h=0 R20=78168390857212609478
APRCL main test (2 42) done: p=3 q=397 k=2 g=5 h=6 R20=21415576708456021294
APRCL main test (2 43) done: p=3 q=463 k=1 g=3 h=1 R20=99991273425398695377
APRCL main test (2 45) done: p=3 q=661 k=1 g=2 h=0 R20=32210149910603768395
APRCL main test (2 47) done: p=3 q=991 k=2 g=6 h=7 R20=43326639831537325863
APRCL main test (2 48) done: p=3 q=1321 k=1 g=13 h=0 R20=35634161447938889271
APRCL main test (2 49) done: p=3 q=2311 k=1 g=3 h=0 R20=78729746622433770854
APRCL main test (2 50) done: p=3 q=2377 k=3 g=5 h=11 R20=36746651772469863344
APRCL main test (2 51) done: p=3 q=2971 k=3 g=10 h=3 R20=26802352559064254472
APRCL main test (2 52) done: p=3 q=3697 k=1 g=5 h=0 R20=24839140662781452611
APRCL main test (2 53) done: p=3 q=4159 k=3 g=3 h=9 R20=757559677096859712
APRCL main test (2 54) done: p=3 q=4621 k=1 g=2 h=2 R20=22679948150625493192
APRCL main test (2 55) done: p=3 q=8317 k=3 g=6 h=6 R20=44516763762057075596
APRCL main test (2 56) done: p=3 q=9241 k=1 g=13 h=2 R20=69194159974378565440
APRCL main test (2 57) done: p=3 q=16633 k=3 g=15 h=24 R20=16110826178980170330
APRCL main test (2 58) done: p=3 q=18481 k=1 g=13 h=0 R20=87001993311175714725
APRCL main test (2 59) done: p=3 q=23761 k=3 g=7 h=18 R20=26255800057028324877
APRCL main test (2 61) done: p=3 q=151 k=1 g=6 h=0 R20=15619773897919593284
APRCL main test (2 63) done: p=3 q=601 k=1 g=7 h=2 R20=30277819795290677154
APRCL main test (2 65) done: p=3 q=1051 k=1 g=7 h=2 R20=78191044603984661073
APRCL main test (2 66) done: p=3 q=1201 k=1 g=11 h=1 R20=79182331222297916719
APRCL main test (2 67) done: p=3 q=1801 k=2 g=11 h=2 R20=71940642973268048210
APRCL main test (2 69) done: p=3 q=3301 k=1 g=6 h=0 R20=29376466880253611547
APRCL main test (2 71) done: p=3 q=4201 k=1 g=11 h=1 R20=90963431025321051505
APRCL main test (2 72) done: p=3 q=4951 k=2 g=6 h=8 R20=3102119750842655851
APRCL main test (2 73) done: p=3 q=6301 k=2 g=10 h=4 R20=98698784089419581801
APRCL main test (2 74) done: p=3 q=9901 k=2 g=2 h=2 R20=13614030240859097817
APRCL main test (2 75) done: p=3 q=11551 k=1 g=7 h=0 R20=78252965111245779586
APRCL main test (2 76) done: p=3 q=12601 k=2 g=11 h=4 R20=62342444804075893887
APRCL main test (2 77) done: p=3 q=14851 k=3 g=2 h=10 R20=45959124260458312075
APRCL main test (2 79) done: p=3 q=19801 k=2 g=13 h=7 R20=95442027032204839830
APRCL main test (2 80) done: p=3 q=97 k=1 g=5 h=2 R20=54660002082682495053
APRCL main test (2 82) done: p=3 q=673 k=1 g=5 h=2 R20=63232623410929503054
APRCL main test (2 83) done: p=3 q=2017 k=2 g=5 h=7 R20=98444835055402133531
APRCL main test (2 84) done: p=3 q=3169 k=2 g=7 h=1 R20=56469285573385836302
APRCL main test (2 85) done: p=3 q=3361 k=1 g=22 h=0 R20=51109428110320701811
APRCL main test (2 86) done: p=3 q=5281 k=1 g=7 h=2 R20=98583066032412747050
APRCL main test (2 87) done: p=3 q=7393 k=1 g=5 h=2 R20=64502457279408449434
APRCL main test (2 88) done: p=3 q=21601 k=3 g=7 h=17 R20=95472746389215847740
APRCL main test (2 89) done: p=3 q=30241 k=3 g=11 h=21 R20=14601721988540674357
APRCL main test (2 91) done: p=3 q=79 k=1 g=3 h=1 R20=13361462728551336146
APRCL main test (2 93) done: p=3 q=157 k=1 g=5 h=1 R20=93932960174998391559
APRCL main test (2 94) done: p=3 q=313 k=1 g=10 h=1 R20=98857585439055087617
APRCL main test (2 96) done: p=3 q=547 k=1 g=2 h=0 R20=61518290768747807139
APRCL main test (2 97) done: p=3 q=859 k=1 g=2 h=1 R20=57088933573217624440
APRCL main test (2 99) done: p=3 q=937 k=2 g=5 h=8 R20=78014908992329418994
APRCL tests for p=3 completed
APRCL main test (3) at level 11 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=65481258869688621755
APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=4 R20=52405427847675506364
APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=1 R20=6230268283479785764
APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=0 R20=3772285289943481085
APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=0 R20=55558360835091642471
APRCL main test (3 16) done: p=5 q=211 k=1 g=2 h=2 R20=41603383626249240229
APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=4 R20=57876837102298479745
APRCL main test (3 18) done: p=5 q=631 k=1 g=3 h=4 R20=350495240250891859
APRCL main test (3 19) done: p=5 q=41 k=1 g=6 h=4 R20=68806446379319669028
APRCL main test (3 21) done: p=5 q=281 k=1 g=3 h=3 R20=3182353543924446015
APRCL main test (3 22) done: p=5 q=2521 k=1 g=17 h=2 R20=84471381738620943579
APRCL main test (3 25) done: p=5 q=241 k=1 g=7 h=4 R20=97234896093386821852
APRCL main test (3 29) done: p=5 q=271 k=1 g=6 h=4 R20=82180281044675592680
APRCL main test (3 32) done: p=5 q=541 k=1 g=2 h=3 R20=49839051507762493443
APRCL main test (3 34) done: p=5 q=2161 k=1 g=23 h=3 R20=47942239214960959076
APRCL main test (3 35) done: p=5 q=7561 k=1 g=13 h=2 R20=5298609289538175283
APRCL main test (3 36) done: p=5 q=15121 k=1 g=11 h=0 R20=45219205182917605987
APRCL main test (3 41) done: p=5 q=331 k=1 g=3 h=2 R20=56278200815946911729
APRCL main test (3 45) done: p=5 q=661 k=1 g=2 h=3 R20=8574802106355865502
APRCL main test (3 46) done: p=5 q=881 k=1 g=3 h=1 R20=31216715307387216952
APRCL main test (3 47) done: p=5 q=991 k=1 g=6 h=1 R20=97682270627577582910
APRCL main test (3 48) done: p=5 q=1321 k=1 g=13 h=4 R20=50240126626297495635
APRCL main test (3 49) done: p=5 q=2311 k=1 g=3 h=3 R20=74164804771309024199
APRCL main test (3 51) done: p=5 q=2971 k=1 g=10 h=0 R20=69297426411834612911
APRCL main test (3 54) done: p=5 q=4621 k=1 g=2 h=2 R20=20745667181204802166
APRCL main test (3 56) done: p=5 q=9241 k=1 g=13 h=4 R20=22258695509065160103
APRCL main test (3 58) done: p=5 q=18481 k=1 g=13 h=0 R20=53925585908935649998
APRCL main test (3 59) done: p=5 q=23761 k=1 g=7 h=3 R20=99192682757521158567
APRCL main test (3 60) done: p=5 q=101 k=2 g=2 h=17 R20=13573109002074313413
APRCL main test (3 61) done: p=5 q=151 k=2 g=6 h=9 R20=64436885092194397568
APRCL main test (3 62) done: p=5 q=401 k=2 g=3 h=22 R20=61364409959686526170
APRCL main test (3 63) done: p=5 q=601 k=2 g=7 h=4 R20=21985969624078522168
APRCL main test (3 64) done: p=5 q=701 k=2 g=2 h=3 R20=18268901014719398390
APRCL main test (3 65) done: p=5 q=1051 k=2 g=7 h=6 R20=26278313176217298570
APRCL main test (3 66) done: p=5 q=1201 k=2 g=11 h=22 R20=72628063046475631131
APRCL main test (3 67) done: p=5 q=1801 k=2 g=11 h=13 R20=97662491371282888359
APRCL main test (3 68) done: p=5 q=2801 k=2 g=3 h=4 R20=98418376499967550922
APRCL main test (3 69) done: p=5 q=3301 k=2 g=6 h=6 R20=24612868003320460177
APRCL main test (3 70) done: p=5 q=3851 k=2 g=2 h=15 R20=59955760871441055543
APRCL main test (3 71) done: p=5 q=4201 k=2 g=11 h=8 R20=39621333636186779831
APRCL main test (3 72) done: p=5 q=4951 k=2 g=6 h=18 R20=74313743069610020507
APRCL main test (3 73) done: p=5 q=6301 k=2 g=10 h=3 R20=74126440189965234637
APRCL main test (3 74) done: p=5 q=9901 k=2 g=2 h=14 R20=40779038982226184737
APRCL main test (3 75) done: p=5 q=11551 k=2 g=7 h=16 R20=912192916464967904
APRCL main test (3 76) done: p=5 q=12601 k=2 g=11 h=22 R20=33434130205509000214
APRCL main test (3 77) done: p=5 q=14851 k=2 g=2 h=5 R20=97118492801901485922
APRCL main test (3 78) done: p=5 q=15401 k=2 g=6 h=13 R20=10173675288181214924
Parameters saved: 2 21621600 3 79 1 1 1808
APRCL main test (3 79) done: p=5 q=19801 k=2 g=13 h=2 R20=12684411290548922184
APRCL main test (3 85) done: p=5 q=3361 k=1 g=22 h=2 R20=13202124779734870666
APRCL main test (3 86) done: p=5 q=5281 k=1 g=7 h=3 R20=20428097053174624189
APRCL main test (3 88) done: p=5 q=21601 k=2 g=7 h=5 R20=64090161722649042581
APRCL main test (3 89) done: p=5 q=30241 k=1 g=11 h=1 R20=72854717817550761255
APRCL main test (3 92) done: p=5 q=131 k=1 g=2 h=2 R20=2466598271038571720
APRCL main test (3 95) done: p=5 q=521 k=1 g=3 h=1 R20=19697176226587774585
APRCL main test (3 98) done: p=5 q=911 k=1 g=17 h=1 R20=58668299193963684921
APRCL tests for p=5 completed
APRCL main test (4) at level 11 for p=7
APRCL L_7 condition satisfied
APRCL main test (4 12) done: p=7 q=29 k=1 g=2 h=1 R20=86697099329843599801
APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=4 R20=51897431558341918436
APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=5 R20=53250451151884748505
APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=4 R20=20101324367128174326
APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=2 R20=57792088736801871271
APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=1 R20=58472736053179584439
APRCL main test (4 18) done: p=7 q=631 k=1 g=3 h=0 R20=59080035279949170113
APRCL main test (4 21) done: p=7 q=281 k=1 g=3 h=3 R20=50620132792173126874
APRCL main test (4 22) done: p=7 q=2521 k=1 g=17 h=6 R20=49576697097742107573
APRCL main test (4 24) done: p=7 q=113 k=1 g=3 h=0 R20=61291852643002447874
APRCL main test (4 26) done: p=7 q=337 k=1 g=10 h=0 R20=94945428839797504628
APRCL main test (4 27) done: p=7 q=1009 k=1 g=11 h=3 R20=50869105362860174577
APRCL main test (4 30) done: p=7 q=379 k=1 g=2 h=3 R20=47836776431896643181
APRCL main test (4 33) done: p=7 q=757 k=1 g=2 h=6 R20=70555697910918211529
APRCL main test (4 35) done: p=7 q=7561 k=1 g=13 h=2 R20=37827228460001599969
APRCL main test (4 36) done: p=7 q=15121 k=1 g=11 h=5 R20=58865473182208448377
APRCL main test (4 43) done: p=7 q=463 k=1 g=3 h=4 R20=51061479313932364473
APRCL main test (4 44) done: p=7 q=617 k=1 g=3 h=5 R20=38852840384313347438
APRCL main test (4 49) done: p=7 q=2311 k=1 g=3 h=0 R20=5464210032574105568
APRCL main test (4 52) done: p=7 q=3697 k=1 g=5 h=6 R20=98786290595094945544
APRCL main test (4 53) done: p=7 q=4159 k=1 g=3 h=1 R20=82672932493466183720
APRCL main test (4 54) done: p=7 q=4621 k=1 g=2 h=1 R20=24005569226108925598
APRCL main test (4 55) done: p=7 q=8317 k=1 g=6 h=4 R20=51706172720627078186
APRCL main test (4 56) done: p=7 q=9241 k=1 g=13 h=0 R20=34090129373581323859
APRCL main test (4 57) done: p=7 q=16633 k=1 g=15 h=5 R20=25860683383500079989
APRCL main test (4 58) done: p=7 q=18481 k=1 g=13 h=2 R20=69563104222871818260
APRCL main test (4 64) done: p=7 q=701 k=1 g=2 h=0 R20=9861882770523055444
APRCL main test (4 65) done: p=7 q=1051 k=1 g=7 h=1 R20=43166656683004885839
APRCL main test (4 68) done: p=7 q=2801 k=1 g=3 h=4 R20=1041287353990124481
APRCL main test (4 70) done: p=7 q=3851 k=1 g=2 h=6 R20=96903047050633469948
APRCL main test (4 71) done: p=7 q=4201 k=1 g=11 h=1 R20=22435544061906911008
APRCL main test (4 73) done: p=7 q=6301 k=1 g=10 h=3 R20=90124755514241246552
APRCL main test (4 75) done: p=7 q=11551 k=1 g=7 h=6 R20=69300044452823849499
APRCL main test (4 76) done: p=7 q=12601 k=1 g=11 h=6 R20=83817519186645932830
APRCL main test (4 78) done: p=7 q=15401 k=1 g=6 h=2 R20=8981985206771123713
APRCL main test (4 82) done: p=7 q=673 k=1 g=5 h=4 R20=79271178863318474781
APRCL main test (4 83) done: p=7 q=2017 k=1 g=5 h=2 R20=48401534055299359299
APRCL main test (4 85) done: p=7 q=3361 k=1 g=22 h=0 R20=75381553168997297861
APRCL main test (4 87) done: p=7 q=7393 k=1 g=5 h=3 R20=40944415731985768738
APRCL main test (4 89) done: p=7 q=30241 k=1 g=11 h=3 R20=78838219321561812493
APRCL main test (4 96) done: p=7 q=547 k=1 g=2 h=3 R20=45349324022525025513
APRCL main test (4 98) done: p=7 q=911 k=1 g=17 h=3 R20=89017904707060318979
APRCL tests for p=7 completed
APRCL main test (5) at level 11 for p=11
APRCL L_11 condition satisfied
APRCL main test (5 37) done: p=11 q=23 k=1 g=5 h=10 R20=84536874344343184089
APRCL main test (5 38) done: p=11 q=67 k=1 g=2 h=1 R20=74754048062853454981
APRCL main test (5 39) done: p=11 q=89 k=1 g=3 h=7 R20=88259473394266383961
APRCL main test (5 40) done: p=11 q=199 k=1 g=3 h=7 R20=27310822689026783089
APRCL main test (5 41) done: p=11 q=331 k=1 g=3 h=0 R20=94644606858641736962
APRCL main test (5 42) done: p=11 q=397 k=1 g=5 h=5 R20=34317303608079645969
APRCL main test (5 43) done: p=11 q=463 k=1 g=3 h=2 R20=10676820328723050498
APRCL main test (5 44) done: p=11 q=617 k=1 g=3 h=8 R20=54132707912384085152
APRCL main test (5 45) done: p=11 q=661 k=1 g=2 h=3 R20=86472854881944043357
APRCL main test (5 46) done: p=11 q=881 k=1 g=3 h=6 R20=94993694811162033689
APRCL main test (5 47) done: p=11 q=991 k=1 g=6 h=4 R20=96743750774151176242
APRCL main test (5 48) done: p=11 q=1321 k=1 g=13 h=8 R20=1721781763461270452
APRCL main test (5 49) done: p=11 q=2311 k=1 g=3 h=0 R20=29282387427581678246
APRCL main test (5 50) done: p=11 q=2377 k=1 g=5 h=8 R20=80839991211605293450
APRCL main test (5 51) done: p=11 q=2971 k=1 g=10 h=6 R20=91987932686184861145
APRCL main test (5 52) done: p=11 q=3697 k=1 g=5 h=4 R20=83928749652226495069
APRCL main test (5 53) done: p=11 q=4159 k=1 g=3 h=7 R20=378093558916139524
APRCL main test (5 54) done: p=11 q=4621 k=1 g=2 h=6 R20=34660495090877073179
APRCL main test (5 55) done: p=11 q=8317 k=1 g=6 h=7 R20=32636646560782105853
APRCL main test (5 56) done: p=11 q=9241 k=1 g=13 h=8 R20=72044702431535196137
APRCL main test (5 57) done: p=11 q=16633 k=1 g=15 h=6 R20=86340507554926235424
APRCL main test (5 58) done: p=11 q=18481 k=1 g=13 h=8 R20=28834739854451612951
APRCL main test (5 59) done: p=11 q=23761 k=1 g=7 h=8 R20=49044335650453455385
APRCL main test (5 69) done: p=11 q=3301 k=1 g=6 h=4 R20=93122682620877988120
APRCL main test (5 70) done: p=11 q=3851 k=1 g=2 h=6 R20=98918633094600185203
APRCL main test (5 72) done: p=11 q=4951 k=1 g=6 h=7 R20=15285366383452372041
APRCL main test (5 74) done: p=11 q=9901 k=1 g=2 h=3 R20=356237667719092416
APRCL main test (5 75) done: p=11 q=11551 k=1 g=7 h=4 R20=67003305493430934984
APRCL main test (5 77) done: p=11 q=14851 k=1 g=2 h=2 R20=61286227157476498482
APRCL main test (5 78) done: p=11 q=15401 k=1 g=6 h=10 R20=71047605537649490941
APRCL main test (5 79) done: p=11 q=19801 k=1 g=13 h=8 R20=96517093922213256412
APRCL main test (5 81) done: p=11 q=353 k=1 g=3 h=6 R20=81091745838732315835
APRCL main test (5 84) done: p=11 q=3169 k=1 g=7 h=5 R20=38092657701697600307
APRCL main test (5 86) done: p=11 q=5281 k=1 g=7 h=8 R20=84194813703482981462
APRCL main test (5 87) done: p=11 q=7393 k=1 g=5 h=0 R20=67413436973417379993
APRCL main test (5 97) done: p=11 q=859 k=1 g=2 h=10 R20=48859412523080212146
APRCL tests for p=11 completed
APRCL main test (6) at level 11 for p=13
APRCL L_13 condition satisfied
APRCL main test (6 90) done: p=13 q=53 k=1 g=2 h=6 R20=36508299279000362845
APRCL main test (6 91) done: p=13 q=79 k=1 g=3 h=0 R20=50901299034732013361
APRCL main test (6 92) done: p=13 q=131 k=1 g=2 h=12 R20=23142613433160384558
APRCL main test (6 93) done: p=13 q=157 k=1 g=5 h=10 R20=55050633320785385842
APRCL main test (6 94) done: p=13 q=313 k=1 g=10 h=10 R20=24039359437333748644
APRCL main test (6 95) done: p=13 q=521 k=1 g=3 h=10 R20=931815016861314773
APRCL main test (6 96) done: p=13 q=547 k=1 g=2 h=1 R20=86249574748667831367
APRCL main test (6 97) done: p=13 q=859 k=1 g=2 h=5 R20=8677494396251519291
APRCL main test (6 98) done: p=13 q=911 k=1 g=17 h=9 R20=36911477239733732932
APRCL main test (6 99) done: p=13 q=937 k=1 g=5 h=1 R20=16925345990554005610
APRCL tests for p=13 completed
Main divisor test: F1=0.0157 F2=0.0008 G=0.5035 S=0.4869 T=21621600
G=2633402496363203103899820345598225927750628035721410542024194304246483753570925014362863311755483439623151204023759263657478475001130343977215545455968507830288609065031007558729165908641905020379259868197615785776971166212975099986359715650021384639960949445679003582045348680048913000
Main divisor test passed: 21621600/21621600
*** N is prime!
Time: 3527 sec

(73*10^2529-37)/99

== ID:B265300350EA8 =============================================

PRIMO 0.1.0 - Primality Certificate

Started 08.10.2001 12:57:57 AM
Running time 91h 29mn 45s

Candidate certified prime

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

Proved prime with 'Primo' by Hans Rosenthal.
The zipped file "737_1264.zip" is 632 KB.
When unpacked the file "Primo-B265300350EA8-001.out" is 1457 KB
and is available on demand by simple email request.

(73*10^14337-37)/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

(73*10^14337-37)/99 is 3-PRP! (53.720000 seconds)
(73*10^14337-37)/99 is 5-PRP! (54.430000 seconds)
(73*10^14337-37)/99 is 7-PRP! (53.550000 seconds)
(73*10^14337-37)/99 is 11-PRP! (53.550000 seconds)
(73*10^14337-37)/99 is 13-PRP! (53.550000 seconds)
(73*10^14337-37)/99 is 17-PRP! (53.490000 seconds)
(73*10^14337-37)/99 is 19-PRP! (53.500000 seconds)
(73*10^14337-37)/99 is 23-PRP! (53.550000 seconds)
(73*10^14337-37)/99 is 29-PRP! (53.550000 seconds)
(73*10^14337-37)/99 is 31-PRP! (53.500000 seconds)
(73*10^14337-37)/99 is 37-PRP! (53.560000 seconds)
(73*10^14337-37)/99 is 41-PRP! (53.940000 seconds)
(73*10^14337-37)/99 is 43-PRP! (53.500000 seconds)
(73*10^14337-37)/99 is 47-PRP! (53.500000 seconds)
(73*10^14337-37)/99 is 53-PRP! (53.500000 seconds)
(73*10^14337-37)/99 is 59-PRP! (53.660000 seconds)
(73*10^14337-37)/99 is 61-PRP! (53.450000 seconds)
(73*10^14337-37)/99 is 251-PRP! (53.550000 seconds)

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Patrick De Geest - Belgium

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