Smoothly Undulating Palindromic Primes

(18*10^3-81)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(18*10^3-81)/99
N=181
*** N is prime!
Time: 0 sec

(18*10^5-81)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(18*10^5-81)/99
N=18181
*** N is prime!
Time: 0 sec

(18*10^77-81)/99
*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(1810^77-81)/99 N=18181818181818181818181818181818181818181818181818181818181818181818181818181 Factor: 2^2 divides N - 1 Factor: 2 divides N + 1 Factor: 3^2 divides N - 1 Factor: 5 divides N - 1 Factor: 11 divides N + 1 Factor: 23 divides N + 1 Factor: 101 divides N - 1 Factor: 463 divides N + 1 Factor: 4093 divides N + 1 Factor: 8779 divides N + 1 Factor: 24179 divides N + 1 Factorization results: F1=0.0559 F2=0.2270 F1=18180 F2=203543218183853614 Pass: gcd(11^((N-1)/2) - 1, N) = 1: R20=81818181818181818179 Pass: 11^(N-1) = 1 (mod N): R20=1 Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=1 q=-3 R20=0 Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=3 q=-1 R20=0 Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=5 q=3 R20=0 Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=7 q=9 R20=0 Pass: gcd(U{(N+1)/2}, N) = 1: d=13 p=9 q=17 R20=41551706097505034510 Pass: U{N+1} = 0 (mod N): d=13 p=9 q=17 R20=0 Pass: gcd(11^((N-1)/3) - 1, N) = 1: R20=47317615823308813516 Pass: gcd(11^((N-1)/5) - 1, N) = 1: R20=92981231529714040336 Pass: gcd(U{(N+1)/11}, N) = 1: d=13 p=9 q=17 R20=67087171817324659228 Pass: gcd(U{(N+1)/23}, N) = 1: d=13 p=9 q=17 R20=98894417935341338082 Pass: gcd(11^((N-1)/101) - 1, N) = 1: R20=70319141650279231014 Pass: gcd(U{(N+1)/463}, N) = 1: d=13 p=9 q=17 R20=17962054882852315644 Pass: gcd(U{(N+1)/4093}, N) = 1: d=13 p=9 q=17 R20=10353649627983941438 Pass: gcd(U{(N+1)/8779}, N) = 1: d=13 p=9 q=17 R20=27307192256137844277 Pass: gcd(U{(N+1)/24179}, N) = 1: d=13 p=9 q=17 R20=81031984508375211758 BLS tests passed: F1=0.0559 F2=0.2270 APRCL test T=1260 S=1723428951244601419 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=2 APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=0 R20=1 APRCL L_2 condition satisfied APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=1 R20=0 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=1 R20=81818181818181818180 APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=1 R20=0 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=3 R20=0 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=81818181818181818179 APRCL main test (1 13) done: p=2 q=43 k=1 g=3 h=1 R20=81818181818181818180 APRCL main test (1 14) done: p=2 q=71 k=1 g=7 h=1 R20=81818181818181818180 APRCL main test (1 15) done: p=2 q=127 k=1 g=3 h=1 R20=81818181818181818180 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=2 R20=81818181818181818178 APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=2 R20=81818181818181818178 APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=0 R20=2 APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=1 R20=1 APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=4 R20=0 APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=6 R20=81818181818181818174 APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=1 R20=0 APRCL main test (2 13) done: p=3 q=43 k=1 g=3 h=1 R20=1 APRCL main test (2 15) done: p=3 q=127 k=2 g=3 h=4 R20=0 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) for p=5 q=11 not needed APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=3 R20=1 APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=0 R20=4 APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=3 R20=1 APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=1 R20=1 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=5 R20=98989857573645346821 APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=0 R20=26038759308785847329 APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=3 R20=89996319552270612729 APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=1 R20=27462122783944923652 APRCL tests for p=7 completed Main divisor test: F1=0.0559 F2=0.2230 G=0.5180 S=0.2391 T=1260 G=3188701780182228764702410847832645437940 Main divisor test passed: 1260/1260 ** N is prime! Time: 1 sec

(18*10^77-81)/99


*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(18*10^77-81)/99
N=18181818181818181818181818181818181818181818181818181818181818181818181818181
Factor: 2^2 divides N - 1
Factor: 2 divides N + 1
Factor: 3^2 divides N - 1
Factor: 5 divides N - 1
Factor: 11 divides N + 1
Factor: 23 divides N + 1
Factor: 101 divides N - 1
Factor: 463 divides N + 1
Factor: 4093 divides N + 1
Factor: 8779 divides N + 1
Factor: 24179 divides N + 1
Factorization results: F1=0.0559 F2=0.2270
F1=18180
F2=203543218183853614
Pass: gcd(11^((N-1)/2) - 1, N) = 1: R20=81818181818181818179
Pass: 11^(N-1) = 1 (mod N): R20=1
Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=1 q=-3 R20=0
Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=3 q=-1 R20=0
Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=5 q=3 R20=0
Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=7 q=9 R20=0
Pass: gcd(U{(N+1)/2}, N) = 1: d=13 p=9 q=17 R20=41551706097505034510
Pass: U{N+1} = 0 (mod N): d=13 p=9 q=17 R20=0
Pass: gcd(11^((N-1)/3) - 1, N) = 1: R20=47317615823308813516
Pass: gcd(11^((N-1)/5) - 1, N) = 1: R20=92981231529714040336
Pass: gcd(U{(N+1)/11}, N) = 1: d=13 p=9 q=17 R20=67087171817324659228
Pass: gcd(U{(N+1)/23}, N) = 1: d=13 p=9 q=17 R20=98894417935341338082
Pass: gcd(11^((N-1)/101) - 1, N) = 1: R20=70319141650279231014
Pass: gcd(U{(N+1)/463}, N) = 1: d=13 p=9 q=17 R20=17962054882852315644
Pass: gcd(U{(N+1)/4093}, N) = 1: d=13 p=9 q=17 R20=10353649627983941438
Pass: gcd(U{(N+1)/8779}, N) = 1: d=13 p=9 q=17 R20=27307192256137844277
Pass: gcd(U{(N+1)/24179}, N) = 1: d=13 p=9 q=17 R20=81031984508375211758
BLS tests passed: F1=0.0559 F2=0.2270
APRCL test
T=1260
S=1723428951244601419
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=2
APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=0 R20=1
APRCL L_2 condition satisfied
APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=1 R20=0
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=1 R20=81818181818181818180
APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=1 R20=0
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=3 R20=0
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=81818181818181818179
APRCL main test (1 13) done: p=2 q=43 k=1 g=3 h=1 R20=81818181818181818180
APRCL main test (1 14) done: p=2 q=71 k=1 g=7 h=1 R20=81818181818181818180
APRCL main test (1 15) done: p=2 q=127 k=1 g=3 h=1 R20=81818181818181818180
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=2 R20=81818181818181818178
APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=2 R20=81818181818181818178
APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=0 R20=2
APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=1 R20=1
APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=4 R20=0
APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=6 R20=81818181818181818174
APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=1 R20=0
APRCL main test (2 13) done: p=3 q=43 k=1 g=3 h=1 R20=1
APRCL main test (2 15) done: p=3 q=127 k=2 g=3 h=4 R20=0
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) for p=5 q=11 not needed
APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=3 R20=1
APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=0 R20=4
APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=3 R20=1
APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=1 R20=1
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=5 R20=98989857573645346821
APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=0 R20=26038759308785847329
APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=3 R20=89996319552270612729
APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=1 R20=27462122783944923652
APRCL tests for p=7 completed
Main divisor test: F1=0.0559 F2=0.2230 G=0.5180 S=0.2391 T=1260
G=3188701780182228764702410847832645437940
Main divisor test passed: 1260/1260
*** N is prime!
Time: 1 sec

(18*10^163-81)/99


*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(18*10^163-81)/99
N=1818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181
Factor: 2^2 divides N - 1
Factor: 2 divides N + 1
Factor: 3^6 divides N - 1
Factor: 5 divides N - 1
Factor: 7 divides N - 1
Factor: 13 divides N - 1
Factor: 19 divides N - 1
Factor: 37 divides N - 1
Factor: 163 divides N - 1
Factor: 653 divides N + 1
Factor: 757 divides N - 1
Factor: 1459 divides N - 1
Factor: 9397 divides N - 1
Factor: 13693 divides N + 1
Factor: 52579 divides N - 1
Factorization results: F1=0.1597 F2=0.0447
F1=82964932842608185486915980
F2=17883058
Pass: gcd(11^((N-1)/2) - 1, N) = 1: R20=81818181818181818179
Pass: 11^(N-1) = 1 (mod N): R20=1
Fail: gcd(U{(N+1)/2}, N) not = 1: d=17 p=1 q=-4 R20=0
Pass: gcd(U{(N+1)/2}, N) = 1: d=17 p=3 q=-2 R20=27132222617234409527
Pass: U{N+1} = 0 (mod N): d=17 p=3 q=-2 R20=0
Fail: gcd(11^((N-1)/3) - 1, N) not = 1: R20=0
Pass: gcd(17^((N-1)/3) - 1, N) = 1: R20=62734444252381646102
Pass: 17^(N-1) = 1 (mod N): R20=1
Pass: gcd(17^((N-1)/5) - 1, N) = 1: R20=42948019280571759968
Pass: gcd(17^((N-1)/7) - 1, N) = 1: R20=77589418762970079009
Pass: gcd(17^((N-1)/13) - 1, N) = 1: R20=62308229638810594724
Pass: gcd(17^((N-1)/19) - 1, N) = 1: R20=5862796054191015113
Pass: gcd(17^((N-1)/37) - 1, N) = 1: R20=70175343976560439937
Pass: gcd(17^((N-1)/163) - 1, N) = 1: R20=83072966486233816488
Pass: gcd(U{(N+1)/653}, N) = 1: d=17 p=3 q=-2 R20=21658127032760361961
Pass: gcd(17^((N-1)/757) - 1, N) = 1: R20=57205070338368334899
Pass: gcd(17^((N-1)/1459) - 1, N) = 1: R20=19931332609148305072
Pass: gcd(17^((N-1)/9397) - 1, N) = 1: R20=54482274270334824084
Pass: gcd(U{(N+1)/13693}, N) = 1: d=17 p=3 q=-2 R20=83559097000931856443
Pass: gcd(17^((N-1)/52579) - 1, N) = 1: R20=22462365843574352086
BLS tests passed: F1=0.1597 F2=0.0447
APRCL test
T=15120
S=8866895254933999141583588658162254776982973249611
APRCL main test (1) at level 7 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=2
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 L_2 condition satisfied
APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=81818181818181818180
APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=1 R20=81818181818181818180
APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=2 R20=81818181818181818179
APRCL main test (1 9) for p=2 q=19 not needed
APRCL main test (1 10) for p=2 q=37 not needed
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=3 R20=0
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=81818181818181818180
APRCL main test (1 17) done: p=2 q=421 k=2 g=2 h=3 R20=0
APRCL main test (1 18) done: p=2 q=631 k=1 g=3 h=1 R20=81818181818181818180
APRCL main test (1 19) done: p=2 q=41 k=3 g=6 h=5 R20=52034973941532918035
APRCL main test (1 20) done: p=2 q=73 k=3 g=5 h=6 R20=13913945969720128408
APRCL main test (1 21) done: p=2 q=281 k=3 g=3 h=5 R20=74036359695132210634
APRCL main test (1 22) done: p=2 q=2521 k=3 g=17 h=1 R20=25681150486021381179
APRCL main test (1 23) done: p=2 q=17 k=4 g=3 h=11 R20=58013104729131289653
APRCL main test (1 24) done: p=2 q=113 k=4 g=3 h=10 R20=50913118266322969685
APRCL main test (1 25) done: p=2 q=241 k=4 g=7 h=4 R20=99162053862673557731
APRCL main test (1 26) done: p=2 q=337 k=4 g=10 h=7 R20=22054185690130885781
APRCL main test (1 27) done: p=2 q=1009 k=4 g=11 h=4 R20=55978518680407775225
APRCL main test (1 28) done: p=2 q=109 k=2 g=6 h=3 R20=0
APRCL main test (1 29) done: p=2 q=271 k=1 g=6 h=1 R20=81818181818181818180
APRCL main test (1 30) done: p=2 q=379 k=1 g=2 h=1 R20=81818181818181818180
APRCL tests for p=2 completed
APRCL main test (2) at level 7 for p=3
APRCL main test (2 4) done: p=3 q=7 k=1 g=3 h=0 R20=2
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=0 R20=2
APRCL L_3 condition satisfied
APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=2 R20=81818181818181818178
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) done: p=3 q=181 k=2 g=2 h=7 R20=0
APRCL main test (2 13) done: p=3 q=43 k=1 g=3 h=1 R20=1
APRCL main test (2 15) done: p=3 q=127 k=2 g=3 h=7 R20=0
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=2 R20=81818181818181818178
APRCL main test (2 18) done: p=3 q=631 k=2 g=3 h=0 R20=6
APRCL main test (2 20) done: p=3 q=73 k=2 g=5 h=1 R20=0
APRCL main test (2 22) done: p=3 q=2521 k=2 g=17 h=8 R20=0
APRCL main test (2 25) done: p=3 q=241 k=1 g=7 h=2 R20=81818181818181818178
APRCL main test (2 26) done: p=3 q=337 k=1 g=10 h=1 R20=1
APRCL main test (2 27) done: p=3 q=1009 k=2 g=11 h=5 R20=0
APRCL main test (2 28) done: p=3 q=109 k=3 g=6 h=2 R20=0
APRCL main test (2 29) done: p=3 q=271 k=3 g=6 h=18 R20=81818181818181818162
APRCL main test (2 30) done: p=3 q=379 k=3 g=2 h=14 R20=0
APRCL tests for p=3 completed
APRCL main test (3) at level 7 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=1
APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=1 R20=1
APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=2 R20=1
APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=0 R20=4
APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=1 R20=1
APRCL main test (3 16) done: p=5 q=211 k=1 g=2 h=3 R20=1
APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=1 R20=1
APRCL main test (3 18) done: p=5 q=631 k=1 g=3 h=1 R20=1
APRCL main test (3 19) done: p=5 q=41 k=1 g=6 h=2 R20=1
APRCL main test (3 21) done: p=5 q=281 k=1 g=3 h=0 R20=4
APRCL main test (3 22) done: p=5 q=2521 k=1 g=17 h=0 R20=4
APRCL main test (3 25) done: p=5 q=241 k=1 g=7 h=0 R20=4
APRCL main test (3 29) done: p=5 q=271 k=1 g=6 h=2 R20=1
APRCL tests for p=5 completed
APRCL main test (4) at level 7 for p=7
APRCL L_7 condition satisfied
APRCL main test (4 12) done: p=7 q=29 k=1 g=2 h=0 R20=6
APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=3 R20=1
APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=5 R20=1
APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=6 R20=81818181818181818170
APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=5 R20=1
APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=1 R20=1
APRCL main test (4 18) done: p=7 q=631 k=1 g=3 h=6 R20=81818181818181818170
APRCL main test (4 21) done: p=7 q=281 k=1 g=3 h=3 R20=1
APRCL main test (4 22) done: p=7 q=2521 k=1 g=17 h=3 R20=1
APRCL main test (4 24) done: p=7 q=113 k=1 g=3 h=6 R20=81818181818181818170
APRCL main test (4 26) done: p=7 q=337 k=1 g=10 h=0 R20=6
APRCL main test (4 27) done: p=7 q=1009 k=1 g=11 h=4 R20=1
APRCL main test (4 30) done: p=7 q=379 k=1 g=2 h=2 R20=1
APRCL tests for p=7 completed
Main divisor test: F1=0.1597 F2=0.0428 G=0.5042 S=0.3017 T=15120
G=6577758637625214552702007661685429351765483131221744497596695028744255670634699620
Main divisor test passed: 15120/15120
*** N is prime!
Time: 10 sec

(18*10^1479-81)/99

== BPI:B263B01E8BA06 ============================================

TITANIX 2.1.0 - Primality Certificate

Started 07.17.2001 at 08:53:49 AM
Running time 15h 20mn 20s

Candidate certified prime

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

Proved prime with Titanix by Hans Rosenthal.
The zipped file "181_739.zip" is 219 KB.
When unpacked the file "Titanix-B263B01E8BA06-001.out" is 516 KB
and is available on demand by simple email request.

(18*10^3657-81)/99

== ID:B26D304492538 =============================================

PRIMO 1.1.0 - Primality Certificate

Started 12.16.2001 07:58:36 PM
Running time 452h 1mn 15s
Started 01.04.2002 05:33:41 PM
Running time 63h 46mn 20s

Candidate certified prime

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

Proved prime with 'Primo' by Hans Rosenthal.
The zipped file "181_1828.zip" is 1268 KB.
When unpacked the file "Primo-B26D304492538.out" is 2908 KB
and is available on demand by simple email request.

(18*10^4573-81)/99

== ID:B2772039178E8 =============================================

PRIMO 1.2.2 - Primality Certificate

Started 05.24.2002 04:37:45 PM
Running time 1576h 30mn 35s

Candidate certified prime

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

 +------------------------------------------------------------------------+
 | Cert_Val a "PRIMO/Titanix" certificate (.out file) validation program  |
 |    Version 1.95 Jim Fougeron, Using the Miracl big integer library     |
 |  Copyright, 2001-2002 Jim Fougeron, Free usage rights granted to all   |
 +------------------------------------------------------------------------+

Processing file primo-b2772039178e8.out

This Certificate is a PRIMO compatible certificate

 1) EC  Test ECtest1 != Ident, ECtest2= Ident	Validated 6mn 34.820s
 2) EC  Test ECtest1 != Ident, ECtest2= Ident	Validated 6mn 34.481s
 ...
 677) EC  Test ECtest1 != Ident, ECtest2= Ident	Validated 0.003s
 678) SPP Test Trial-div to 518403  !Success!!!	Validated 0.003s

Prime number being certified was:
N=(18*10^4573-81)/99

Certificate for this number was FULLY validated!
Total time used to validate certificate: 18h 38mn 7.905s
There were 678 steps in the primality proof

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

Proved prime with 'Primo 1.2.2' by Hans Rosenthal.
The zipped file "181_2286.zip" is 2186 KB.
When unpacked the file "Primo-B2772039178E8.out" is 4987 KB
and is available on demand by simple email request.

(18*10^8315-81)/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

(18*10^8315-81)/99 is 3-PRP! (16.590000 seconds)
(18*10^8315-81)/99 is 5-PRP! (16.590000 seconds)
(18*10^8315-81)/99 is 7-PRP! (16.590000 seconds)
(18*10^8315-81)/99 is 11-PRP! (16.530000 seconds)
(18*10^8315-81)/99 is 13-PRP! (16.590000 seconds)
(18*10^8315-81)/99 is 17-PRP! (16.590000 seconds)
(18*10^8315-81)/99 is 19-PRP! (16.590000 seconds)
(18*10^8315-81)/99 is 23-PRP! (16.580000 seconds)
(18*10^8315-81)/99 is 29-PRP! (16.530000 seconds)
(18*10^8315-81)/99 is 31-PRP! (16.590000 seconds)
(18*10^8315-81)/99 is 37-PRP! (16.530000 seconds)
(18*10^8315-81)/99 is 41-PRP! (16.590000 seconds)
(18*10^8315-81)/99 is 43-PRP! (16.580000 seconds)
(18*10^8315-81)/99 is 47-PRP! (16.530000 seconds)
(18*10^8315-81)/99 is 53-PRP! (16.530000 seconds)
(18*10^8315-81)/99 is 59-PRP! (16.590000 seconds)
(18*10^8315-81)/99 is 61-PRP! (16.590000 seconds)
(18*10^8315-81)/99 is 251-PRP! (16.590000 seconds)

(18*10^30259-81)/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, 67,
71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, and 251

(18*10^30259-81)/99 is 3-PRP! (347.240000 seconds)
(18*10^30259-81)/99 is 5-PRP! (349.880000 seconds)
(18*10^30259-81)/99 is 7-PRP! (351.800000 seconds)
(18*10^30259-81)/99 is 11-PRP! (349.760000 seconds)
(18*10^30259-81)/99 is 13-PRP! (349.050000 seconds)
(18*10^30259-81)/99 is 17-PRP! (349.490000 seconds)
(18*10^30259-81)/99 is 19-PRP! (348.720000 seconds)
(18*10^30259-81)/99 is 23-PRP! (348.890000 seconds)
(18*10^30259-81)/99 is 29-PRP! (349.380000 seconds)
(18*10^30259-81)/99 is 31-PRP! (350.970000 seconds)
(18*10^30259-81)/99 is 37-PRP! (348.340000 seconds)
(18*10^30259-81)/99 is 41-PRP! (350.370000 seconds)
(18*10^30259-81)/99 is 43-PRP! (353.830000 seconds)
(18*10^30259-81)/99 is 47-PRP! (349.710000 seconds)
(18*10^30259-81)/99 is 53-PRP! (347.510000 seconds)
(18*10^30259-81)/99 is 59-PRP! (348.340000 seconds)
(18*10^30259-81)/99 is 61-PRP! (350.150000 seconds)
(18*10^30259-81)/99 is 67-PRP! (349.060000 seconds)
(18*10^30259-81)/99 is 71-PRP! (349.440000 seconds)
(18*10^30259-81)/99 is 73-PRP! (349.110000 seconds)
(18*10^30259-81)/99 is 79-PRP! (352.620000 seconds)
(18*10^30259-81)/99 is 83-PRP! (352.570000 seconds)
(18*10^30259-81)/99 is 89-PRP! (348.770000 seconds)
(18*10^30259-81)/99 is 97-PRP! (348.010000 seconds)
(18*10^30259-81)/99 is 101-PRP! (347.130000 seconds)
(18*10^30259-81)/99 is 103-PRP! (348.780000 seconds)
(18*10^30259-81)/99 is 107-PRP! (349.390000 seconds)
(18*10^30259-81)/99 is 109-PRP! (348.830000 seconds)
(18*10^30259-81)/99 is 113-PRP! (350.150000 seconds)
(18*10^30259-81)/99 is 127-PRP! (349.110000 seconds)
(18*10^30259-81)/99 is 251-PRP! (350.480000 seconds)

(18*10^31063-81)/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, 67,
71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, and 251

(18*10^31063-81)/99 is 3-PRP! (358.500000 seconds)
(18*10^31063-81)/99 is 5-PRP! (357.120000 seconds)
(18*10^31063-81)/99 is 7-PRP! (357.620000 seconds)
(18*10^31063-81)/99 is 11-PRP! (357.900000 seconds)
(18*10^31063-81)/99 is 13-PRP! (363.330000 seconds)
(18*10^31063-81)/99 is 17-PRP! (358.610000 seconds)
(18*10^31063-81)/99 is 19-PRP! (356.910000 seconds)
(18*10^31063-81)/99 is 23-PRP! (360.370000 seconds)
(18*10^31063-81)/99 is 29-PRP! (357.230000 seconds)
(18*10^31063-81)/99 is 31-PRP! (358.670000 seconds)
(18*10^31063-81)/99 is 37-PRP! (359.100000 seconds)
(18*10^31063-81)/99 is 41-PRP! (359.540000 seconds)
(18*10^31063-81)/99 is 43-PRP! (358.610000 seconds)
(18*10^31063-81)/99 is 47-PRP! (360.470000 seconds)
(18*10^31063-81)/99 is 53-PRP! (355.260000 seconds)
(18*10^31063-81)/99 is 59-PRP! (356.850000 seconds)
(18*10^31063-81)/99 is 61-PRP! (358.170000 seconds)
(18*10^31063-81)/99 is 67-PRP! (358.880000 seconds)
(18*10^31063-81)/99 is 71-PRP! (355.810000 seconds)
(18*10^31063-81)/99 is 73-PRP! (359.480000 seconds)
(18*10^31063-81)/99 is 79-PRP! (359.430000 seconds)
(18*10^31063-81)/99 is 83-PRP! (359.590000 seconds)
(18*10^31063-81)/99 is 89-PRP! (359.820000 seconds)
(18*10^31063-81)/99 is 97-PRP! (358.000000 seconds)
(18*10^31063-81)/99 is 101-PRP! (356.080000 seconds)
(18*10^31063-81)/99 is 103-PRP! (357.790000 seconds)
(18*10^31063-81)/99 is 107-PRP! (359.870000 seconds)
(18*10^31063-81)/99 is 109-PRP! (357.620000 seconds)
(18*10^31063-81)/99 is 113-PRP! (357.620000 seconds)
(18*10^31063-81)/99 is 127-PRP! (358.330000 seconds)
(18*10^31063-81)/99 is 251-PRP! (356.190000 seconds)

(18*10^31855-81)/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, 67,
71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, and 251

(18*10^31855-81)/99 is 3-PRP! (367.950000 seconds)
(18*10^31855-81)/99 is 5-PRP! (366.350000 seconds)
(18*10^31855-81)/99 is 7-PRP! (363.990000 seconds)
(18*10^31855-81)/99 is 11-PRP! (364.710000 seconds)
(18*10^31855-81)/99 is 13-PRP! (366.130000 seconds)
(18*10^31855-81)/99 is 17-PRP! (365.480000 seconds)
(18*10^31855-81)/99 is 19-PRP! (368.550000 seconds)
(18*10^31855-81)/99 is 23-PRP! (365.310000 seconds)
(18*10^31855-81)/99 is 29-PRP! (365.310000 seconds)
(18*10^31855-81)/99 is 31-PRP! (366.900000 seconds)
(18*10^31855-81)/99 is 37-PRP! (362.510000 seconds)
(18*10^31855-81)/99 is 41-PRP! (368.440000 seconds)
(18*10^31855-81)/99 is 43-PRP! (363.720000 seconds)
(18*10^31855-81)/99 is 47-PRP! (366.360000 seconds)
(18*10^31855-81)/99 is 53-PRP! (365.420000 seconds)
(18*10^31855-81)/99 is 59-PRP! (364.870000 seconds)
(18*10^31855-81)/99 is 61-PRP! (363.780000 seconds)
(18*10^31855-81)/99 is 67-PRP! (363.990000 seconds)
(18*10^31855-81)/99 is 71-PRP! (364.920000 seconds)
(18*10^31855-81)/99 is 73-PRP! (364.270000 seconds)
(18*10^31855-81)/99 is 79-PRP! (363.830000 seconds)
(18*10^31855-81)/99 is 83-PRP! (365.530000 seconds)
(18*10^31855-81)/99 is 89-PRP! (366.850000 seconds)
(18*10^31855-81)/99 is 97-PRP! (365.690000 seconds)
(18*10^31855-81)/99 is 101-PRP! (362.950000 seconds)
(18*10^31855-81)/99 is 103-PRP! (364.760000 seconds)
(18*10^31855-81)/99 is 107-PRP! (366.190000 seconds)
(18*10^31855-81)/99 is 109-PRP! (362.890000 seconds)
(18*10^31855-81)/99 is 113-PRP! (364.100000 seconds)
(18*10^31855-81)/99 is 127-PRP! (365.030000 seconds)
(18*10^31855-81)/99 is 251-PRP! (365.690000 seconds)

(18*10^36915-81)/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, 67,
71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, and 251

(18*10^36915-81)/99 is 3-PRP! (519.920000 seconds)
(18*10^36915-81)/99 is 5-PRP! (527.400000 seconds)
(18*10^36915-81)/99 is 7-PRP! (518.280000 seconds)
(18*10^36915-81)/99 is 11-PRP! (520.200000 seconds)
(18*10^36915-81)/99 is 13-PRP! (515.140000 seconds)
(18*10^36915-81)/99 is 17-PRP! (522.450000 seconds)
(18*10^36915-81)/99 is 19-PRP! (517.230000 seconds)
(18*10^36915-81)/99 is 23-PRP! (518.770000 seconds)
(18*10^36915-81)/99 is 29-PRP! (522.460000 seconds)
(18*10^36915-81)/99 is 31-PRP! (526.350000 seconds)
(18*10^36915-81)/99 is 37-PRP! (523.720000 seconds)
(18*10^36915-81)/99 is 41-PRP! (519.050000 seconds)
(18*10^36915-81)/99 is 43-PRP! (523.600000 seconds)
(18*10^36915-81)/99 is 47-PRP! (528.380000 seconds)
(18*10^36915-81)/99 is 53-PRP! (525.360000 seconds)
(18*10^36915-81)/99 is 59-PRP! (524.860000 seconds)
(18*10^36915-81)/99 is 61-PRP! (525.470000 seconds)
(18*10^36915-81)/99 is 67-PRP! (520.310000 seconds)
(18*10^36915-81)/99 is 71-PRP! (521.190000 seconds)
(18*10^36915-81)/99 is 73-PRP! (522.730000 seconds)
(18*10^36915-81)/99 is 79-PRP! (517.180000 seconds)
(18*10^36915-81)/99 is 83-PRP! (521.190000 seconds)
(18*10^36915-81)/99 is 89-PRP! (535.140000 seconds)
(18*10^36915-81)/99 is 97-PRP! (518.500000 seconds)
(18*10^36915-81)/99 is 101-PRP! (514.270000 seconds)
(18*10^36915-81)/99 is 103-PRP! (516.400000 seconds)
(18*10^36915-81)/99 is 107-PRP! (520.750000 seconds)
(18*10^36915-81)/99 is 109-PRP! (522.390000 seconds)
(18*10^36915-81)/99 is 113-PRP! (516.960000 seconds)
(18*10^36915-81)/99 is 127-PRP! (520.590000 seconds)
(18*10^36915-81)/99 is 251-PRP! (515.370000 seconds)

(18*10^66657-81)/99

By Ray Chandler

PFGW Version 3.4.4.64BIT.20101104.Win_Dev [GWNUM 26.4]

Primality testing (18*10^66657-81)/99 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.10% and helper 0.03% (0.34% proof)
(18*10^66657-81)/99 is Fermat and Lucas PRP! (1392.6408s+0.0182s)

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Patrick De Geest - Belgium

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