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(14*10^11-41)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(14*10^11-41)/99 N=14141414141 Factor: 2^2 divides N - 1 Factor: 2 divides N + 1 Factor: 3^2 divides N + 1 Factor: 5 divides N - 1 Factor: 7 divides N - 1 Factor: 41 divides N - 1 Factorization results: F1=0.3703 F2=0.1237 F1=5740 F2=18 Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=14141414139 Pass: 3^(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=8242449012 Pass: U{N+1} = 0 (mod N): d=17 p=3 q=-2 R20=0 Pass: gcd(U{(N+1)/3}, N) = 1: d=17 p=3 q=-2 R20=2267746005 Pass: gcd(3^((N-1)/5) - 1, N) = 1: R20=12435979405 Pass: gcd(3^((N-1)/7) - 1, N) = 1: R20=13728603784 Pass: gcd(3^((N-1)/41) - 1, N) = 1: R20=7317607937 BLS tests passed: F1=0.3703 F2=0.1237 Main divisor test: F1=0.3703 F2=0.0940 G=0.4643 S=0.0000 T=1 G=51660 Main divisor test passed: 1/1 Final divisor test: F=0.3703 G=0.4643 H=1.2050 t=-1 a=1 Final divisor test passed: 3/3 r=3 i=0 *** N is prime! Time: 0 sec
(14*10^277-41)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(14*10^277-41)/99 N=1414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141 Factor: 2^2 divides N - 1 Factor: 2 divides N + 1 Factor: 3 divides N - 1 Factor: 5 divides N - 1 Factor: 7^2 divides N - 1 Factor: 13 divides N - 1 Factor: 37 divides N - 1 Factor: 47 divides N - 1 Factor: 101 divides N - 1 Factor: 139 divides N - 1 Factor: 277 divides N - 1 Factor: 401 divides N + 1 Factor: 829 divides N - 1 Factor: 1289 divides N - 1 Factor: 2531 divides N - 1 Factor: 9901 divides N - 1 Factor: 31051 divides N - 1 Factorization results: F1=0.1171 F2=0.0105 F1=214911894516004225824069639448140 F2=802 Pass: gcd(17^((N-1)/2) - 1, N) = 1: R20=41414141414141414139 Pass: 17^(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=84566989162681520261 Pass: U{N+1} = 0 (mod N): d=17 p=3 q=-2 R20=0 Pass: gcd(17^((N-1)/3) - 1, N) = 1: R20=80602032751583786477 Pass: gcd(17^((N-1)/5) - 1, N) = 1: R20=1946316348586274137 Pass: gcd(17^((N-1)/7) - 1, N) = 1: R20=50200045454666893484 Pass: gcd(17^((N-1)/13) - 1, N) = 1: R20=37750803700988282534 Pass: gcd(17^((N-1)/37) - 1, N) = 1: R20=59790382542396186062 Pass: gcd(17^((N-1)/47) - 1, N) = 1: R20=48944368259892400294 Pass: gcd(17^((N-1)/101) - 1, N) = 1: R20=70472749579370541571 Pass: gcd(17^((N-1)/139) - 1, N) = 1: R20=47829677929501984344 Pass: gcd(17^((N-1)/277) - 1, N) = 1: R20=85667731139713393817 Pass: gcd(U{(N+1)/401}, N) = 1: d=17 p=3 q=-2 R20=43685712283374687571 Pass: gcd(17^((N-1)/829) - 1, N) = 1: R20=53160156737090191785 Pass: gcd(17^((N-1)/1289) - 1, N) = 1: R20=45380099254022858671 Pass: gcd(17^((N-1)/2531) - 1, N) = 1: R20=18583403170735620636 Pass: gcd(17^((N-1)/9901) - 1, N) = 1: R20=73464213256280358123 Pass: gcd(17^((N-1)/31051) - 1, N) = 1: R20=21806878165580285642 BLS tests passed: F1=0.1171 F2=0.0105 APRCL test T=166320 S=146553969618403723064076944652330914417086303108539659462070325167889553352957789468906401433605097936013 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=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 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 L_2 condition satisfied 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=0 R20=1 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=0 R20=2 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=1 R20=41414141414141414140 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=1 R20=41414141414141414140 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=0 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=4 R20=2112777779332735679 APRCL main test (1 20) done: p=2 q=73 k=3 g=5 h=7 R20=36118335781445197271 APRCL main test (1 21) done: p=2 q=281 k=3 g=3 h=1 R20=74689470246746659924 APRCL main test (1 22) done: p=2 q=2521 k=3 g=17 h=3 R20=87355172375145885433 APRCL main test (1 23) done: p=2 q=17 k=4 g=3 h=13 R20=98601128282088839628 APRCL main test (1 24) done: p=2 q=113 k=4 g=3 h=10 R20=33297499174847968640 APRCL main test (1 25) done: p=2 q=241 k=4 g=7 h=10 R20=18343227419145862685 APRCL main test (1 26) done: p=2 q=337 k=4 g=10 h=4 R20=3552181084099491380 APRCL main test (1 27) done: p=2 q=1009 k=4 g=11 h=7 R20=8338793167147764500 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=1 R20=41414141414141414140 APRCL main test (1 31) done: p=2 q=433 k=4 g=5 h=11 R20=92157548407077630023 APRCL main test (1 32) done: p=2 q=541 k=2 g=2 h=2 R20=41414141414141414139 APRCL main test (1 33) done: p=2 q=757 k=2 g=2 h=1 R20=0 APRCL main test (1 34) done: p=2 q=2161 k=4 g=23 h=1 R20=50402163487947560003 APRCL main test (1 35) done: p=2 q=7561 k=3 g=13 h=1 R20=70166737655367306857 APRCL main test (1 36) done: p=2 q=15121 k=4 g=11 h=4 R20=48499286544860746101 APRCL main test (1 37) done: p=2 q=23 k=1 g=5 h=1 R20=41414141414141414140 APRCL main test (1 38) done: p=2 q=67 k=1 g=2 h=1 R20=41414141414141414140 APRCL main test (1 39) done: p=2 q=89 k=3 g=3 h=1 R20=96908009532029448691 APRCL main test (1 40) done: p=2 q=199 k=1 g=3 h=0 R20=1 APRCL main test (1 41) done: p=2 q=331 k=1 g=3 h=1 R20=41414141414141414140 APRCL main test (1 42) done: p=2 q=397 k=2 g=5 h=0 R20=2 APRCL main test (1 43) done: p=2 q=463 k=1 g=3 h=1 R20=41414141414141414140 APRCL main test (1 44) done: p=2 q=617 k=3 g=3 h=0 R20=79073766361425973170 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=13 R20=51374744038671488927 APRCL main test (1 47) done: p=2 q=991 k=1 g=6 h=0 R20=1 APRCL main test (1 48) done: p=2 q=1321 k=3 g=13 h=1 R20=41463527234721552838 APRCL main test (1 49) done: p=2 q=2311 k=1 g=3 h=0 R20=1 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) done: p=3 q=19 k=2 g=2 h=8 R20=36174606893258344212 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=2 R20=3072461360075105570 APRCL main test (2 13) done: p=3 q=43 k=1 g=3 h=2 R20=41414141414141414138 APRCL main test (2 15) done: p=3 q=127 k=2 g=3 h=8 R20=53393472953856847595 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=0 R20=2 APRCL main test (2 18) done: p=3 q=631 k=2 g=3 h=8 R20=58845512531651565202 APRCL main test (2 20) done: p=3 q=73 k=2 g=5 h=3 R20=96984355834703280807 APRCL main test (2 22) done: p=3 q=2521 k=2 g=17 h=3 R20=24321048505056759839 APRCL main test (2 25) done: p=3 q=241 k=1 g=7 h=0 R20=2 APRCL main test (2 26) done: p=3 q=337 k=1 g=10 h=2 R20=41414141414141414138 APRCL main test (2 27) done: p=3 q=1009 k=2 g=11 h=0 R20=29681339650556853954 APRCL main test (2 28) done: p=3 q=109 k=3 g=6 h=24 R20=77945704308643442140 APRCL main test (2 29) done: p=3 q=271 k=3 g=6 h=25 R20=52692959961407384494 APRCL main test (2 30) done: p=3 q=379 k=3 g=2 h=8 R20=54432149522085015766 APRCL main test (2 31) done: p=3 q=433 k=3 g=5 h=12 R20=62252342851943330978 APRCL main test (2 32) done: p=3 q=541 k=3 g=2 h=21 R20=56145304935552470392 APRCL main test (2 33) done: p=3 q=757 k=3 g=2 h=9 R20=38111045681018542137 APRCL main test (2 34) done: p=3 q=2161 k=3 g=23 h=21 R20=58394305553595367483 APRCL main test (2 35) done: p=3 q=7561 k=3 g=13 h=12 R20=71159063047123771235 APRCL main test (2 36) done: p=3 q=15121 k=3 g=11 h=21 R20=18465092752762933292 APRCL main test (2 38) done: p=3 q=67 k=1 g=2 h=1 R20=1 APRCL main test (2 40) done: p=3 q=199 k=2 g=3 h=8 R20=47099101319099597429 APRCL main test (2 41) done: p=3 q=331 k=1 g=3 h=2 R20=41414141414141414138 APRCL main test (2 42) done: p=3 q=397 k=2 g=5 h=6 R20=38384848235734646186 APRCL main test (2 43) done: p=3 q=463 k=1 g=3 h=0 R20=2 APRCL main test (2 45) done: p=3 q=661 k=1 g=2 h=0 R20=2 APRCL main test (2 47) done: p=3 q=991 k=2 g=6 h=6 R20=39108940044054863212 APRCL main test (2 48) done: p=3 q=1321 k=1 g=13 h=2 R20=41414141414141414138 APRCL main test (2 49) done: p=3 q=2311 k=1 g=3 h=1 R20=1 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=1 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=1 R20=1 APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=1 R20=1 APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=4 R20=41414141414141414134 APRCL main test (3 16) done: p=5 q=211 k=1 g=2 h=1 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=2 R20=1 APRCL main test (3 22) done: p=5 q=2521 k=1 g=17 h=3 R20=1 APRCL main test (3 25) done: p=5 q=241 k=1 g=7 h=1 R20=1 APRCL main test (3 29) done: p=5 q=271 k=1 g=6 h=4 R20=41414141414141414134 APRCL main test (3 32) done: p=5 q=541 k=1 g=2 h=3 R20=1 APRCL main test (3 34) done: p=5 q=2161 k=1 g=23 h=1 R20=1 APRCL main test (3 35) done: p=5 q=7561 k=1 g=13 h=4 R20=41414141414141414134 APRCL main test (3 36) done: p=5 q=15121 k=1 g=11 h=4 R20=41414141414141414134 APRCL main test (3 41) done: p=5 q=331 k=1 g=3 h=2 R20=1 APRCL main test (3 45) done: p=5 q=661 k=1 g=2 h=2 R20=1 APRCL main test (3 46) done: p=5 q=881 k=1 g=3 h=0 R20=4 APRCL main test (3 47) done: p=5 q=991 k=1 g=6 h=1 R20=1 APRCL main test (3 48) done: p=5 q=1321 k=1 g=13 h=0 R20=4 APRCL main test (3 49) done: p=5 q=2311 k=1 g=3 h=2 R20=1 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=5 R20=1 APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=2 R20=1 APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=4 R20=1 APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=6 R20=41414141414141414130 APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=0 R20=6 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=2 R20=1 APRCL main test (4 21) done: p=7 q=281 k=1 g=3 h=2 R20=1 APRCL main test (4 22) done: p=7 q=2521 k=1 g=17 h=6 R20=41414141414141414130 APRCL main test (4 24) done: p=7 q=113 k=1 g=3 h=6 R20=41414141414141414130 APRCL main test (4 26) done: p=7 q=337 k=1 g=10 h=4 R20=1 APRCL main test (4 27) done: p=7 q=1009 k=1 g=11 h=5 R20=1 APRCL main test (4 30) done: p=7 q=379 k=1 g=2 h=4 R20=1 APRCL main test (4 33) done: p=7 q=757 k=1 g=2 h=1 R20=1 APRCL main test (4 35) done: p=7 q=7561 k=1 g=13 h=4 R20=1 APRCL main test (4 36) done: p=7 q=15121 k=1 g=11 h=4 R20=1 APRCL main test (4 43) done: p=7 q=463 k=1 g=3 h=4 R20=1 APRCL main test (4 44) done: p=7 q=617 k=1 g=3 h=5 R20=1 APRCL main test (4 49) done: p=7 q=2311 k=1 g=3 h=2 R20=1 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=47027851994409430460 APRCL main test (5 38) done: p=11 q=67 k=1 g=2 h=9 R20=91125633911633144172 APRCL main test (5 39) done: p=11 q=89 k=1 g=3 h=7 R20=31993641578924614313 APRCL main test (5 40) done: p=11 q=199 k=1 g=3 h=6 R20=25368404792167925010 APRCL main test (5 41) done: p=11 q=331 k=1 g=3 h=7 R20=61179657139688322577 APRCL main test (5 42) done: p=11 q=397 k=1 g=5 h=2 R20=11784131593735748202 APRCL main test (5 43) done: p=11 q=463 k=1 g=3 h=8 R20=89526031856987768686 APRCL main test (5 44) done: p=11 q=617 k=1 g=3 h=3 R20=57529293577047465017 APRCL main test (5 45) done: p=11 q=661 k=1 g=2 h=0 R20=45291849716232133206 APRCL main test (5 46) done: p=11 q=881 k=1 g=3 h=1 R20=28281184563822450582 APRCL main test (5 47) done: p=11 q=991 k=1 g=6 h=3 R20=9804912941943028955 APRCL main test (5 48) done: p=11 q=1321 k=1 g=13 h=7 R20=89100801443771440448 APRCL main test (5 49) done: p=11 q=2311 k=1 g=3 h=8 R20=93812521648702604304 APRCL tests for p=11 completed Main divisor test: F1=0.1171 F2=0.0094 G=0.5037 S=0.3772 T=166320 G=12629972695072359674911099014053241782977538098061268854099242964582263554914902421086400057644732067402058888649614405146337305939098193820 Main divisor test passed: 166320/166320 *** N is prime! Time: 93 sec
(14*10^479-41)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(14*10^479-41)/99 N=14141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141 Factor: 2^2 divides N - 1 Factor: 2 divides N + 1 Factor: 3^2 divides N + 1 Factor: 5 divides N - 1 Factor: 7 divides N - 1 Factor: 11 divides N + 1 Factor: 479 divides N - 1 Factorization results: F1=0.0101 F2=0.0048 F1=67060 F2=198 Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=41414141414141414139 Pass: 3^(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=15802130095320573300 Pass: U{N+1} = 0 (mod N): d=17 p=3 q=-2 R20=0 Pass: gcd(U{(N+1)/3}, N) = 1: d=17 p=3 q=-2 R20=96431638876567028556 Pass: gcd(3^((N-1)/5) - 1, N) = 1: R20=53780944316392876406 Pass: gcd(3^((N-1)/7) - 1, N) = 1: R20=15078425032964281908 Pass: gcd(U{(N+1)/11}, N) = 1: d=17 p=3 q=-2 R20=18568910294036955051 Pass: gcd(3^((N-1)/479) - 1, N) = 1: R20=61934381129352531262 BLS tests passed: F1=0.0101 F2=0.0048 APRCL test T=1663200 S=76535246469267219944930671091611929197891238428008431781519703242486122147499852206907091486726766752777581864591909228403946260835874657007800515214660479424456606296335394592714218007842175294289839385991109282956026209962304696457 APRCL main test (1) at level 10 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=41414141414141414140 APRCL main test (1 3) for p=2 q=5 not needed APRCL main test (1 4) for p=2 q=7 not needed APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=2 R20=41414141414141414139 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=41414141414141414140 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=41414141414141414140 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 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=1 R20=41414141414141414140 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=2 R20=41414141414141414139 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=4 R20=82112672256672403889 APRCL main test (1 20) done: p=2 q=73 k=3 g=5 h=7 R20=9939289386041035201 APRCL main test (1 21) done: p=2 q=281 k=3 g=3 h=0 R20=31720129537155243405 APRCL main test (1 22) done: p=2 q=2521 k=3 g=17 h=3 R20=10458351411864199596 APRCL main test (1 23) done: p=2 q=17 k=4 g=3 h=5 R20=66131286735212143806 APRCL main test (1 24) done: p=2 q=113 k=4 g=3 h=3 R20=79980667487292350474 APRCL main test (1 25) done: p=2 q=241 k=4 g=7 h=4 R20=22456738382971940493 APRCL main test (1 26) done: p=2 q=337 k=4 g=10 h=2 R20=76209366798072649498 APRCL main test (1 27) done: p=2 q=1009 k=4 g=11 h=10 R20=87046547603150538288 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=41414141414141414140 APRCL main test (1 30) done: p=2 q=379 k=1 g=2 h=1 R20=41414141414141414140 APRCL main test (1 31) done: p=2 q=433 k=4 g=5 h=1 R20=13320944863988912470 APRCL main test (1 32) done: p=2 q=541 k=2 g=2 h=1 R20=0 APRCL main test (1 33) done: p=2 q=757 k=2 g=2 h=2 R20=41414141414141414139 APRCL main test (1 34) done: p=2 q=2161 k=4 g=23 h=4 R20=62581431761567086787 APRCL main test (1 35) done: p=2 q=7561 k=3 g=13 h=4 R20=64482574814297235466 APRCL main test (1 36) done: p=2 q=15121 k=4 g=11 h=1 R20=10619060654502095542 APRCL main test (1 37) done: p=2 q=23 k=1 g=5 h=1 R20=41414141414141414140 APRCL main test (1 38) done: p=2 q=67 k=1 g=2 h=1 R20=41414141414141414140 APRCL main test (1 39) done: p=2 q=89 k=3 g=3 h=5 R20=62876705118941892091 APRCL main test (1 40) done: p=2 q=199 k=1 g=3 h=1 R20=41414141414141414140 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=41414141414141414139 APRCL main test (1 43) done: p=2 q=463 k=1 g=3 h=1 R20=41414141414141414140 APRCL main test (1 44) done: p=2 q=617 k=3 g=3 h=7 R20=63508567867158306134 APRCL main test (1 45) done: p=2 q=661 k=2 g=2 h=0 R20=2 APRCL main test (1 46) done: p=2 q=881 k=4 g=3 h=3 R20=90207003753615553169 APRCL main test (1 47) done: p=2 q=991 k=1 g=6 h=0 R20=1 APRCL main test (1 48) done: p=2 q=1321 k=3 g=13 h=6 R20=34391111044850370138 APRCL main test (1 49) done: p=2 q=2311 k=1 g=3 h=0 R20=1 APRCL main test (1 50) done: p=2 q=2377 k=3 g=5 h=3 R20=1908059610486135903 APRCL main test (1 51) done: p=2 q=2971 k=1 g=10 h=1 R20=41414141414141414140 APRCL main test (1 52) done: p=2 q=3697 k=4 g=5 h=2 R20=86615755421112953950 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=0 R20=2 APRCL main test (1 55) done: p=2 q=8317 k=2 g=6 h=0 R20=2 APRCL main test (1 56) done: p=2 q=9241 k=3 g=13 h=7 R20=28270703607258220028 APRCL main test (1 57) done: p=2 q=16633 k=3 g=15 h=7 R20=99549318805825789572 APRCL main test (1 58) done: p=2 q=18481 k=4 g=13 h=1 R20=43401504752173993567 APRCL main test (1 59) done: p=2 q=23761 k=4 g=7 h=2 R20=65006669159909870437 APRCL main test (1 60) done: p=2 q=101 k=2 g=2 h=1 R20=0 APRCL main test (1 61) done: p=2 q=151 k=1 g=6 h=0 R20=1 APRCL main test (1 62) done: p=2 q=401 k=4 g=3 h=11 R20=76311201975933293222 APRCL main test (1 63) done: p=2 q=601 k=3 g=7 h=2 R20=49239549770058122770 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=0 R20=1 APRCL main test (1 66) done: p=2 q=1201 k=4 g=11 h=13 R20=11143358127630042136 APRCL main test (1 67) done: p=2 q=1801 k=3 g=11 h=1 R20=90934852107839719200 APRCL main test (1 68) done: p=2 q=2801 k=4 g=3 h=10 R20=44824315792061200080 APRCL main test (1 69) done: p=2 q=3301 k=2 g=6 h=3 R20=0 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=5 R20=47689476594153368910 APRCL main test (1 72) done: p=2 q=4951 k=1 g=6 h=1 R20=41414141414141414140 APRCL main test (1 73) done: p=2 q=6301 k=2 g=10 h=1 R20=0 APRCL main test (1 74) done: p=2 q=9901 k=2 g=2 h=1 R20=0 APRCL main test (1 75) done: p=2 q=11551 k=1 g=7 h=0 R20=1 APRCL main test (1 76) done: p=2 q=12601 k=3 g=11 h=7 R20=23774881109093749094 APRCL main test (1 77) done: p=2 q=14851 k=1 g=2 h=0 R20=1 APRCL main test (1 78) done: p=2 q=15401 k=3 g=6 h=2 R20=13407300674065531614 APRCL main test (1 79) done: p=2 q=19801 k=3 g=13 h=5 R20=11010133790460854296 APRCL main test (1 80) done: p=2 q=97 k=5 g=5 h=21 R20=3324788544056513285 APRCL main test (1 81) done: p=2 q=353 k=5 g=3 h=27 R20=61548608978072008425 APRCL main test (1 82) done: p=2 q=673 k=5 g=5 h=21 R20=83353803211949142604 APRCL main test (1 83) done: p=2 q=2017 k=5 g=5 h=8 R20=26185049794668400543 APRCL main test (1 84) done: p=2 q=3169 k=5 g=7 h=26 R20=52626573486185904373 APRCL main test (1 85) done: p=2 q=3361 k=5 g=22 h=9 R20=66255128090406213351 APRCL main test (1 86) done: p=2 q=5281 k=5 g=7 h=29 R20=23299359782696661966 APRCL tests for p=2 completed APRCL main test (2) at level 10 for p=3 APRCL main test (2 4) done: p=3 q=7 k=1 g=3 h=0 R20=1010101010101010100 APRCL L_3 condition satisfied APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=2 R20=75602175602175602176 APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=2 R20=97784294558488106875 APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=0 R20=56217916873654578572 APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=1 R20=92219737511239651501 APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=7 R20=43279384203357085881 APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=3 R20=11300280563597776634 APRCL main test (2 13) done: p=3 q=43 k=1 g=3 h=2 R20=45407564012215175006 APRCL main test (2 15) done: p=3 q=127 k=2 g=3 h=5 R20=50702528357985651988 APRCL main test (2 16) done: p=3 q=211 k=1 g=2 h=2 R20=38369476758102350519 APRCL main test (2 17) done: p=3 q=421 k=1 g=2 h=0 R20=69368266992970080856 APRCL main test (2 18) done: p=3 q=631 k=2 g=3 h=6 R20=33923307344255615439 APRCL main test (2 20) done: p=3 q=73 k=2 g=5 h=8 R20=28606252569648834035 APRCL main test (2 22) done: p=3 q=2521 k=2 g=17 h=5 R20=20705777242829408958 APRCL main test (2 25) done: p=3 q=241 k=1 g=7 h=2 R20=13956997359486986043 APRCL main test (2 26) done: p=3 q=337 k=1 g=10 h=0 R20=63789227587447172017 APRCL main test (2 27) done: p=3 q=1009 k=2 g=11 h=2 R20=66983002730744899041 APRCL main test (2 28) done: p=3 q=109 k=3 g=6 h=5 R20=67595181141181151067 APRCL main test (2 29) done: p=3 q=271 k=3 g=6 h=10 R20=5703517356390200778 APRCL main test (2 30) done: p=3 q=379 k=3 g=2 h=0 R20=38948895822802213223 APRCL main test (2 31) done: p=3 q=433 k=3 g=5 h=19 R20=90890446363197478769 APRCL main test (2 32) done: p=3 q=541 k=3 g=2 h=7 R20=65595315895366522172 APRCL main test (2 33) done: p=3 q=757 k=3 g=2 h=11 R20=86784986324389057951 APRCL main test (2 34) done: p=3 q=2161 k=3 g=23 h=26 R20=56811952861547484792 APRCL main test (2 35) done: p=3 q=7561 k=3 g=13 h=24 R20=87830129431079536300 APRCL main test (2 36) done: p=3 q=15121 k=3 g=11 h=2 R20=92246466922321228219 APRCL main test (2 38) done: p=3 q=67 k=1 g=2 h=2 R20=41610131162369968340 APRCL main test (2 40) done: p=3 q=199 k=2 g=3 h=0 R20=31101270983605344031 APRCL main test (2 41) done: p=3 q=331 k=1 g=3 h=1 R20=30800451646373096524 APRCL main test (2 42) done: p=3 q=397 k=2 g=5 h=8 R20=46752849031855246814 APRCL main test (2 43) done: p=3 q=463 k=1 g=3 h=0 R20=62412461548530663001 APRCL main test (2 45) done: p=3 q=661 k=1 g=2 h=0 R20=24251593086691422546 APRCL main test (2 47) done: p=3 q=991 k=2 g=6 h=2 R20=35344917733663116806 APRCL main test (2 48) done: p=3 q=1321 k=1 g=13 h=1 R20=17316235787091199657 APRCL main test (2 49) done: p=3 q=2311 k=1 g=3 h=0 R20=64404320137768861265 APRCL main test (2 50) done: p=3 q=2377 k=3 g=5 h=19 R20=8902646223265281634 APRCL main test (2 51) done: p=3 q=2971 k=3 g=10 h=1 R20=76503374898145472196 APRCL main test (2 52) done: p=3 q=3697 k=1 g=5 h=1 R20=51835913913273934913 APRCL main test (2 53) done: p=3 q=4159 k=3 g=3 h=2 R20=38053571227547616948 APRCL main test (2 54) done: p=3 q=4621 k=1 g=2 h=2 R20=88448212923434736895 APRCL main test (2 55) done: p=3 q=8317 k=3 g=6 h=5 R20=76810141844098759353 APRCL main test (2 56) done: p=3 q=9241 k=1 g=13 h=2 R20=71013566024928431594 APRCL main test (2 57) done: p=3 q=16633 k=3 g=15 h=5 R20=79966349234737889460 APRCL main test (2 58) done: p=3 q=18481 k=1 g=13 h=2 R20=21215947145279973590 APRCL main test (2 59) done: p=3 q=23761 k=3 g=7 h=4 R20=43999659676507552144 APRCL main test (2 61) done: p=3 q=151 k=1 g=6 h=1 R20=12268379155796374339 APRCL main test (2 63) done: p=3 q=601 k=1 g=7 h=0 R20=71552463066606161448 APRCL main test (2 65) done: p=3 q=1051 k=1 g=7 h=1 R20=82136301165796884160 APRCL main test (2 66) done: p=3 q=1201 k=1 g=11 h=2 R20=13592208513107763732 APRCL main test (2 67) done: p=3 q=1801 k=2 g=11 h=1 R20=14517411165217385916 APRCL main test (2 69) done: p=3 q=3301 k=1 g=6 h=1 R20=62388195802312736575 APRCL main test (2 71) done: p=3 q=4201 k=1 g=11 h=2 R20=60313922370575548390 APRCL main test (2 72) done: p=3 q=4951 k=2 g=6 h=6 R20=68896458700549889850 APRCL main test (2 73) done: p=3 q=6301 k=2 g=10 h=2 R20=7015470183545359481 APRCL main test (2 74) done: p=3 q=9901 k=2 g=2 h=7 R20=57746011728257088664 APRCL main test (2 75) done: p=3 q=11551 k=1 g=7 h=1 R20=88668172505069743404 APRCL main test (2 76) done: p=3 q=12601 k=2 g=11 h=0 R20=99609111871285674811 APRCL main test (2 77) done: p=3 q=14851 k=3 g=2 h=4 R20=50305512512839628090 APRCL main test (2 79) done: p=3 q=19801 k=2 g=13 h=7 R20=43010575910238941831 APRCL main test (2 80) done: p=3 q=97 k=1 g=5 h=0 R20=66541705716963448922 APRCL main test (2 82) done: p=3 q=673 k=1 g=5 h=1 R20=10108514566166869287 APRCL main test (2 83) done: p=3 q=2017 k=2 g=5 h=5 R20=25748994604581674416 APRCL main test (2 84) done: p=3 q=3169 k=2 g=7 h=0 R20=42959860962512089530 APRCL main test (2 85) done: p=3 q=3361 k=1 g=22 h=0 R20=14077700540062932208 APRCL main test (2 86) done: p=3 q=5281 k=1 g=7 h=1 R20=19846639085419619409 APRCL tests for p=3 completed APRCL main test (3) at level 10 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=1 APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=1 R20=1 APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=4 R20=41414141414141414134 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=1 R20=1 APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=3 R20=1 APRCL main test (3 18) done: p=5 q=631 k=1 g=3 h=3 R20=1 APRCL main test (3 19) done: p=5 q=41 k=1 g=6 h=1 R20=1 APRCL main test (3 21) done: p=5 q=281 k=1 g=3 h=4 R20=41414141414141414134 APRCL main test (3 22) done: p=5 q=2521 k=1 g=17 h=3 R20=1 APRCL main test (3 25) done: p=5 q=241 k=1 g=7 h=3 R20=1 APRCL main test (3 29) done: p=5 q=271 k=1 g=6 h=1 R20=1 APRCL main test (3 32) done: p=5 q=541 k=1 g=2 h=3 R20=1 APRCL main test (3 34) done: p=5 q=2161 k=1 g=23 h=0 R20=4 APRCL main test (3 35) done: p=5 q=7561 k=1 g=13 h=4 R20=41414141414141414134 APRCL main test (3 36) done: p=5 q=15121 k=1 g=11 h=2 R20=1 APRCL main test (3 41) done: p=5 q=331 k=1 g=3 h=2 R20=1 APRCL main test (3 45) done: p=5 q=661 k=1 g=2 h=0 R20=4 APRCL main test (3 46) done: p=5 q=881 k=1 g=3 h=3 R20=1 APRCL main test (3 47) done: p=5 q=991 k=1 g=6 h=1 R20=1 APRCL main test (3 48) done: p=5 q=1321 k=1 g=13 h=4 R20=41414141414141414134 APRCL main test (3 49) done: p=5 q=2311 k=1 g=3 h=1 R20=1 APRCL main test (3 51) done: p=5 q=2971 k=1 g=10 h=4 R20=41414141414141414134 APRCL main test (3 54) done: p=5 q=4621 k=1 g=2 h=0 R20=4 APRCL main test (3 56) done: p=5 q=9241 k=1 g=13 h=1 R20=1 APRCL main test (3 58) done: p=5 q=18481 k=1 g=13 h=0 R20=4 APRCL main test (3 59) done: p=5 q=23761 k=1 g=7 h=3 R20=1 APRCL main test (3 60) done: p=5 q=101 k=2 g=2 h=23 R20=46384429148232259598 APRCL main test (3 61) done: p=5 q=151 k=2 g=6 h=23 R20=99524727150000803627 APRCL main test (3 62) done: p=5 q=401 k=2 g=3 h=9 R20=61324324870925623980 APRCL main test (3 63) done: p=5 q=601 k=2 g=7 h=24 R20=71907493952485579125 APRCL main test (3 64) done: p=5 q=701 k=2 g=2 h=17 R20=47405467306333827435 APRCL main test (3 65) done: p=5 q=1051 k=2 g=7 h=0 R20=5793478193524681741 APRCL main test (3 66) done: p=5 q=1201 k=2 g=11 h=1 R20=66879665959721726001 APRCL main test (3 67) done: p=5 q=1801 k=2 g=11 h=12 R20=45538619885912306092 APRCL main test (3 68) done: p=5 q=2801 k=2 g=3 h=17 R20=98050172080041117690 APRCL main test (3 69) done: p=5 q=3301 k=2 g=6 h=20 R20=54702101188196827139 APRCL main test (3 70) done: p=5 q=3851 k=2 g=2 h=3 R20=22362083108301453805 APRCL main test (3 71) done: p=5 q=4201 k=2 g=11 h=8 R20=95573767984389579313 APRCL main test (3 72) done: p=5 q=4951 k=2 g=6 h=20 R20=83662032419222799561 APRCL main test (3 73) done: p=5 q=6301 k=2 g=10 h=14 R20=40648185276096523735 APRCL main test (3 74) done: p=5 q=9901 k=2 g=2 h=23 R20=36884401807440171330 APRCL main test (3 75) done: p=5 q=11551 k=2 g=7 h=4 R20=95875223375229193584 APRCL main test (3 76) done: p=5 q=12601 k=2 g=11 h=3 R20=4455889775169439271 APRCL main test (3 77) done: p=5 q=14851 k=2 g=2 h=9 R20=69225731950354172437 APRCL main test (3 78) done: p=5 q=15401 k=2 g=6 h=6 R20=11679977086074279352 APRCL main test (3 79) done: p=5 q=19801 k=2 g=13 h=7 R20=16428029153652834776 APRCL main test (3 85) done: p=5 q=3361 k=1 g=22 h=0 R20=4 APRCL main test (3 86) done: p=5 q=5281 k=1 g=7 h=3 R20=1 APRCL tests for p=5 completed APRCL main test (4) at level 10 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=41414141414141414130 APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=2 R20=1 APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=2 R20=1 APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=5 R20=1 APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=6 R20=41414141414141414130 APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=6 R20=41414141414141414130 APRCL main test (4 18) done: p=7 q=631 k=1 g=3 h=1 R20=1 APRCL main test (4 21) done: p=7 q=281 k=1 g=3 h=4 R20=1 APRCL main test (4 22) done: p=7 q=2521 k=1 g=17 h=2 R20=1 APRCL main test (4 24) done: p=7 q=113 k=1 g=3 h=0 R20=6 APRCL main test (4 26) done: p=7 q=337 k=1 g=10 h=2 R20=1 APRCL main test (4 27) done: p=7 q=1009 k=1 g=11 h=2 R20=1 APRCL main test (4 30) done: p=7 q=379 k=1 g=2 h=6 R20=41414141414141414130 APRCL main test (4 33) done: p=7 q=757 k=1 g=2 h=2 R20=1 APRCL main test (4 35) done: p=7 q=7561 k=1 g=13 h=4 R20=1 APRCL main test (4 36) done: p=7 q=15121 k=1 g=11 h=3 R20=1 APRCL main test (4 43) done: p=7 q=463 k=1 g=3 h=1 R20=1 APRCL main test (4 44) done: p=7 q=617 k=1 g=3 h=0 R20=6 APRCL main test (4 49) done: p=7 q=2311 k=1 g=3 h=4 R20=1 APRCL main test (4 52) done: p=7 q=3697 k=1 g=5 h=1 R20=1 APRCL main test (4 53) done: p=7 q=4159 k=1 g=3 h=3 R20=1 APRCL main test (4 54) done: p=7 q=4621 k=1 g=2 h=0 R20=6 APRCL main test (4 55) done: p=7 q=8317 k=1 g=6 h=0 R20=6 APRCL main test (4 56) done: p=7 q=9241 k=1 g=13 h=5 R20=1 APRCL main test (4 57) done: p=7 q=16633 k=1 g=15 h=0 R20=6 APRCL main test (4 58) done: p=7 q=18481 k=1 g=13 h=6 R20=41414141414141414130 APRCL main test (4 64) done: p=7 q=701 k=1 g=2 h=1 R20=1 APRCL main test (4 65) done: p=7 q=1051 k=1 g=7 h=2 R20=1 APRCL main test (4 68) done: p=7 q=2801 k=1 g=3 h=4 R20=1 APRCL main test (4 70) done: p=7 q=3851 k=1 g=2 h=6 R20=41414141414141414130 APRCL main test (4 71) done: p=7 q=4201 k=1 g=11 h=6 R20=41414141414141414130 APRCL main test (4 73) done: p=7 q=6301 k=1 g=10 h=4 R20=1 APRCL main test (4 75) done: p=7 q=11551 k=1 g=7 h=2 R20=1 APRCL main test (4 76) done: p=7 q=12601 k=1 g=11 h=5 R20=1 APRCL main test (4 78) done: p=7 q=15401 k=1 g=6 h=1 R20=1 APRCL main test (4 82) done: p=7 q=673 k=1 g=5 h=3 R20=1 APRCL main test (4 83) done: p=7 q=2017 k=1 g=5 h=0 R20=6 APRCL main test (4 85) done: p=7 q=3361 k=1 g=22 h=3 R20=1 APRCL tests for p=7 completed APRCL main test (5) at level 10 for p=11 APRCL L_11 condition satisfied APRCL main test (5 37) done: p=11 q=23 k=1 g=5 h=5 R20=15841766459388583028 APRCL main test (5 38) done: p=11 q=67 k=1 g=2 h=2 R20=66435951495793965442 APRCL main test (5 39) done: p=11 q=89 k=1 g=3 h=8 R20=78846730203642138172 APRCL main test (5 40) done: p=11 q=199 k=1 g=3 h=7 R20=61919074352207268961 APRCL main test (5 41) done: p=11 q=331 k=1 g=3 h=4 R20=19172085033958650496 APRCL main test (5 42) done: p=11 q=397 k=1 g=5 h=4 R20=39279812396283601533 APRCL main test (5 43) done: p=11 q=463 k=1 g=3 h=10 R20=77421361916606725285 APRCL main test (5 44) done: p=11 q=617 k=1 g=3 h=2 R20=69400653558286340122 APRCL main test (5 45) done: p=11 q=661 k=1 g=2 h=8 R20=85739228648225956205 APRCL main test (5 46) done: p=11 q=881 k=1 g=3 h=10 R20=55903982363093234730 APRCL main test (5 47) done: p=11 q=991 k=1 g=6 h=2 R20=88296412535999187066 APRCL main test (5 48) done: p=11 q=1321 k=1 g=13 h=2 R20=68314453175110429929 APRCL main test (5 49) done: p=11 q=2311 k=1 g=3 h=0 R20=55738681185618483561 APRCL main test (5 50) done: p=11 q=2377 k=1 g=5 h=4 R20=53488557941999447631 APRCL main test (5 51) done: p=11 q=2971 k=1 g=10 h=6 R20=87618699359240803464 APRCL main test (5 52) done: p=11 q=3697 k=1 g=5 h=8 R20=72235975262108118570 APRCL main test (5 53) done: p=11 q=4159 k=1 g=3 h=0 R20=30754216001895086243 APRCL main test (5 54) done: p=11 q=4621 k=1 g=2 h=1 R20=16445546356631493331 APRCL main test (5 55) done: p=11 q=8317 k=1 g=6 h=6 R20=68591225669183825965 APRCL main test (5 56) done: p=11 q=9241 k=1 g=13 h=1 R20=41456320758654234371 APRCL main test (5 57) done: p=11 q=16633 k=1 g=15 h=8 R20=80209498715304662192 APRCL main test (5 58) done: p=11 q=18481 k=1 g=13 h=5 R20=94995660572554439757 APRCL main test (5 59) done: p=11 q=23761 k=1 g=7 h=0 R20=16261758124600499480 APRCL main test (5 69) done: p=11 q=3301 k=1 g=6 h=9 R20=1538866877571312283 APRCL main test (5 70) done: p=11 q=3851 k=1 g=2 h=8 R20=53711793839483505118 APRCL main test (5 72) done: p=11 q=4951 k=1 g=6 h=7 R20=29224791818280883939 APRCL main test (5 74) done: p=11 q=9901 k=1 g=2 h=9 R20=23731960842076598774 APRCL main test (5 75) done: p=11 q=11551 k=1 g=7 h=1 R20=28547807294156078891 APRCL main test (5 77) done: p=11 q=14851 k=1 g=2 h=9 R20=35885282853287239380 APRCL main test (5 78) done: p=11 q=15401 k=1 g=6 h=10 R20=47695487243783871537 APRCL main test (5 79) done: p=11 q=19801 k=1 g=13 h=1 R20=19115165953434658588 APRCL main test (5 81) done: p=11 q=353 k=1 g=3 h=2 R20=67570208065364094176 APRCL main test (5 84) done: p=11 q=3169 k=1 g=7 h=6 R20=87524459059983185050 APRCL main test (5 86) done: p=11 q=5281 k=1 g=7 h=3 R20=6144942582064107727 APRCL tests for p=11 completed Main divisor test: F1=0.0101 F2=0.0042 G=0.5013 S=0.4871 T=1663200 G=508112909194676917181198029536946101229048058449242298091602418644670815769922668810523765954889800865685199344113809852820094988913721695395367152479218043270201941804992904577354130500983731248272586293231815062988080646367143141496235580 Main divisor test passed: 1663200/1663200 *** N is prime! Time: 1423 sec
(14*10^583-41)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(14*10^583-41)/99 N=1414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141 Factor: 2^2 divides N - 1 Factor: 2 divides N + 1 Factor: 3 divides N - 1 Factor: 5 divides N - 1 Factor: 7^2 divides N - 1 Factor: 13 divides N - 1 Factor: 37 divides N - 1 Factor: 1747 divides N - 1 Factor: 18043 divides N - 1 Factorization results: F1=0.0234 F2=0.0005 F1=44575278050940 F2=2 Pass: gcd(11^((N-1)/2) - 1, N) = 1: R20=41414141414141414139 Pass: 11^(N-1) = 1 (mod N): R20=1 Pass: gcd(11^((N-1)/3) - 1, N) = 1: R20=20872340301607564100 Fail: gcd(11^((N-1)/5) - 1, N) not = 1: R20=0 Pass: gcd(33^((N-1)/5) - 1, N) = 1: R20=74070798512313003040 Pass: 33^(N-1) = 1 (mod N): R20=1 Pass: gcd(33^((N-1)/7) - 1, N) = 1: R20=26189140928904677139 Fail: gcd(33^((N-1)/13) - 1, N) not = 1: R20=0 Pass: gcd(47^((N-1)/13) - 1, N) = 1: R20=83266373794736546976 Pass: 47^(N-1) = 1 (mod N): R20=1 Pass: gcd(47^((N-1)/37) - 1, N) = 1: R20=53375668226674230482 Pass: gcd(47^((N-1)/1747) - 1, N) = 1: R20=41626528608618044692 Pass: gcd(47^((N-1)/18043) - 1, N) = 1: R20=22365387695068441706 BLS tests passed: F1=0.0234 F2=0.0005 APRCL test T=21621600 S=837194590636416249975976779942064409721406197507566651006363766324159412287263231790318134877271387087777680948260455797171219426160433531381442409643335081586473272562970076601785872243885253724076725355473371784773217440565046985719391613199376299897336057967649035618378893909 APRCL main test (1) at level 11 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=41414141414141414140 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=0 R20=1 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=3 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=1 R20=41414141414141414140 APRCL main test (1 15) done: p=2 q=127 k=1 g=3 h=1 R20=41414141414141414140 APRCL main test (1 16) done: p=2 q=211 k=1 g=2 h=1 R20=41414141414141414140 APRCL main test (1 17) done: p=2 q=421 k=2 g=2 h=0 R20=2 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=4 R20=63008263593203366949 APRCL main test (1 20) done: p=2 q=73 k=3 g=5 h=7 R20=3218324243207439318 APRCL main test (1 21) done: p=2 q=281 k=3 g=3 h=7 R20=24610540613382845960 APRCL main test (1 22) done: p=2 q=2521 k=3 g=17 h=3 R20=66524869711952267323 APRCL main test (1 23) done: p=2 q=17 k=4 g=3 h=12 R20=63220768567181894380 APRCL main test (1 24) done: p=2 q=113 k=4 g=3 h=12 R20=40820689355023601241 APRCL main test (1 25) done: p=2 q=241 k=4 g=7 h=2 R20=70638182218962550885 APRCL main test (1 26) done: p=2 q=337 k=4 g=10 h=2 R20=88063685167187670566 APRCL main test (1 27) done: p=2 q=1009 k=4 g=11 h=0 R20=19555502400365807441 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=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=5 R20=90308628119441011599 APRCL main test (1 32) done: p=2 q=541 k=2 g=2 h=2 R20=41414141414141414139 APRCL main test (1 33) done: p=2 q=757 k=2 g=2 h=0 R20=2 APRCL main test (1 34) done: p=2 q=2161 k=4 g=23 h=8 R20=56596489109021501671 APRCL main test (1 35) done: p=2 q=7561 k=3 g=13 h=1 R20=88208867034707202723 APRCL main test (1 36) done: p=2 q=15121 k=4 g=11 h=10 R20=47859425037108536481 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=4 R20=26893514139135474210 APRCL main test (1 40) done: p=2 q=199 k=1 g=3 h=0 R20=1 APRCL main test (1 41) done: p=2 q=331 k=1 g=3 h=1 R20=41414141414141414140 APRCL main test (1 42) done: p=2 q=397 k=2 g=5 h=1 R20=0 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=0 R20=75709122936912182177 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=2 R20=33726907579789383394 APRCL main test (1 47) done: p=2 q=991 k=1 g=6 h=1 R20=41414141414141414140 APRCL main test (1 48) done: p=2 q=1321 k=3 g=13 h=2 R20=86735683990489326872 APRCL main test (1 49) done: p=2 q=2311 k=1 g=3 h=1 R20=41414141414141414140 APRCL main test (1 50) done: p=2 q=2377 k=3 g=5 h=1 R20=93212733421436483732 APRCL main test (1 51) done: p=2 q=2971 k=1 g=10 h=1 R20=41414141414141414140 APRCL main test (1 52) done: p=2 q=3697 k=4 g=5 h=10 R20=76287445400022397337 APRCL main test (1 53) done: p=2 q=4159 k=1 g=3 h=1 R20=41414141414141414140 APRCL main test (1 54) done: p=2 q=4621 k=2 g=2 h=2 R20=41414141414141414139 APRCL main test (1 55) done: p=2 q=8317 k=2 g=6 h=3 R20=0 APRCL main test (1 56) done: p=2 q=9241 k=3 g=13 h=4 R20=61007384366412956406 APRCL main test (1 57) done: p=2 q=16633 k=3 g=15 h=0 R20=60659356089451976349 APRCL main test (1 58) done: p=2 q=18481 k=4 g=13 h=2 R20=96440292305658811427 APRCL main test (1 59) done: p=2 q=23761 k=4 g=7 h=15 R20=56195649814516181753 APRCL main test (1 60) done: p=2 q=101 k=2 g=2 h=1 R20=0 APRCL main test (1 61) done: p=2 q=151 k=1 g=6 h=0 R20=1 APRCL main test (1 62) done: p=2 q=401 k=4 g=3 h=8 R20=79709687541694236380 APRCL main test (1 63) done: p=2 q=601 k=3 g=7 h=5 R20=70768815861942899110 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=0 R20=1 APRCL main test (1 66) done: p=2 q=1201 k=4 g=11 h=12 R20=71647577376972314078 APRCL main test (1 67) done: p=2 q=1801 k=3 g=11 h=3 R20=20284656976964002288 APRCL main test (1 68) done: p=2 q=2801 k=4 g=3 h=15 R20=12769193374507819942 APRCL main test (1 69) done: p=2 q=3301 k=2 g=6 h=2 R20=41414141414141414139 APRCL main test (1 70) done: p=2 q=3851 k=1 g=2 h=1 R20=41414141414141414140 APRCL main test (1 71) done: p=2 q=4201 k=3 g=11 h=5 R20=77790193464528623101 APRCL main test (1 72) done: p=2 q=4951 k=1 g=6 h=1 R20=41414141414141414140 APRCL main test (1 73) done: p=2 q=6301 k=2 g=10 h=2 R20=41414141414141414139 APRCL main test (1 74) done: p=2 q=9901 k=2 g=2 h=1 R20=0 APRCL main test (1 75) done: p=2 q=11551 k=1 g=7 h=0 R20=1 APRCL main test (1 76) done: p=2 q=12601 k=3 g=11 h=0 R20=93418557869385810282 APRCL main test (1 77) done: p=2 q=14851 k=1 g=2 h=1 R20=41414141414141414140 APRCL main test (1 78) done: p=2 q=15401 k=3 g=6 h=2 R20=37296397478155486146 APRCL main test (1 79) done: p=2 q=19801 k=3 g=13 h=0 R20=30777161597337230012 APRCL main test (1 80) done: p=2 q=97 k=5 g=5 h=24 R20=53794239695664751169 APRCL main test (1 81) done: p=2 q=353 k=5 g=3 h=14 R20=53818543020119636901 APRCL main test (1 82) done: p=2 q=673 k=5 g=5 h=11 R20=61574595267965301024 APRCL main test (1 83) done: p=2 q=2017 k=5 g=5 h=10 R20=58220591814308522163 APRCL main test (1 84) done: p=2 q=3169 k=5 g=7 h=19 R20=79187019782631510255 APRCL main test (1 85) done: p=2 q=3361 k=5 g=22 h=20 R20=27820315101100987451 APRCL main test (1 86) done: p=2 q=5281 k=5 g=7 h=3 R20=12535976985377625153 APRCL main test (1 87) done: p=2 q=7393 k=5 g=5 h=20 R20=64846258149219745502 APRCL main test (1 88) done: p=2 q=21601 k=5 g=7 h=30 R20=77640903463513155162 APRCL main test (1 89) done: p=2 q=30241 k=5 g=11 h=5 R20=25372951403864138971 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=1 R20=41414141414141414140 APRCL main test (1 93) done: p=2 q=157 k=2 g=5 h=1 R20=0 APRCL main test (1 94) done: p=2 q=313 k=3 g=10 h=0 R20=74334186710763208567 APRCL main test (1 95) done: p=2 q=521 k=3 g=3 h=6 R20=793140088962891636 APRCL main test (1 96) done: p=2 q=547 k=1 g=2 h=0 R20=1 APRCL main test (1 97) done: p=2 q=859 k=1 g=2 h=1 R20=41414141414141414140 APRCL main test (1 98) done: p=2 q=911 k=1 g=17 h=1 R20=41414141414141414140 APRCL main test (1 99) done: p=2 q=937 k=3 g=5 h=1 R20=40291852897043968940 APRCL main test (1 100) done: p=2 q=1093 k=2 g=5 h=2 R20=41414141414141414139 APRCL main test (1 101) done: p=2 q=1171 k=1 g=2 h=1 R20=41414141414141414140 APRCL main test (1 102) done: p=2 q=1249 k=5 g=7 h=18 R20=3661375803867824034 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) 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=2 R20=41414141414141414138 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=8 R20=41519798274577111519 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=15528372442187393318 APRCL main test (2 13) done: p=3 q=43 k=1 g=3 h=2 R20=41414141414141414138 APRCL main test (2 15) done: p=3 q=127 k=2 g=3 h=7 R20=441786452629565723 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=41414141414141414138 APRCL main test (2 18) done: p=3 q=631 k=2 g=3 h=5 R20=98804172520328171764 APRCL main test (2 20) done: p=3 q=73 k=2 g=5 h=7 R20=34429227492155233333 APRCL main test (2 22) done: p=3 q=2521 k=2 g=17 h=5 R20=13423723915974269597 APRCL main test (2 25) done: p=3 q=241 k=1 g=7 h=2 R20=41414141414141414138 APRCL main test (2 26) done: p=3 q=337 k=1 g=10 h=2 R20=41414141414141414138 APRCL main test (2 27) done: p=3 q=1009 k=2 g=11 h=1 R20=72205537723006200214 APRCL main test (2 28) done: p=3 q=109 k=3 g=6 h=3 R20=65802759503032687594 APRCL main test (2 29) done: p=3 q=271 k=3 g=6 h=3 R20=50936421557726861430 APRCL main test (2 30) done: p=3 q=379 k=3 g=2 h=9 R20=32046408413034937318 APRCL main test (2 31) done: p=3 q=433 k=3 g=5 h=13 R20=40723813210533409236 APRCL main test (2 32) done: p=3 q=541 k=3 g=2 h=4 R20=32808847408412170138 APRCL main test (2 33) done: p=3 q=757 k=3 g=2 h=4 R20=53400514361062826572 APRCL main test (2 34) done: p=3 q=2161 k=3 g=23 h=19 R20=39844694262628299689 APRCL main test (2 35) done: p=3 q=7561 k=3 g=13 h=15 R20=48422611765910863931 APRCL main test (2 36) done: p=3 q=15121 k=3 g=11 h=14 R20=22082900290621703400 APRCL main test (2 38) done: p=3 q=67 k=1 g=2 h=1 R20=1 APRCL main test (2 40) done: p=3 q=199 k=2 g=3 h=5 R20=19577030809550161859 APRCL main test (2 41) done: p=3 q=331 k=1 g=3 h=2 R20=41414141414141414138 APRCL main test (2 42) done: p=3 q=397 k=2 g=5 h=5 R20=63289604670396054164 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=41414141414141414138 APRCL main test (2 47) done: p=3 q=991 k=2 g=6 h=6 R20=65154646670781744035 APRCL main test (2 48) done: p=3 q=1321 k=1 g=13 h=0 R20=2 APRCL main test (2 49) done: p=3 q=2311 k=1 g=3 h=0 R20=2 APRCL main test (2 50) done: p=3 q=2377 k=3 g=5 h=12 R20=31544504104717641360 APRCL main test (2 51) done: p=3 q=2971 k=3 g=10 h=12 R20=68891027929127939686 APRCL main test (2 52) done: p=3 q=3697 k=1 g=5 h=1 R20=1 APRCL main test (2 53) done: p=3 q=4159 k=3 g=3 h=2 R20=97915513744495047443 APRCL main test (2 54) done: p=3 q=4621 k=1 g=2 h=1 R20=1 APRCL main test (2 55) done: p=3 q=8317 k=3 g=6 h=10 R20=61075880133295090999 APRCL main test (2 56) done: p=3 q=9241 k=1 g=13 h=1 R20=1 APRCL main test (2 57) done: p=3 q=16633 k=3 g=15 h=22 R20=42893785541959067128 APRCL main test (2 58) done: p=3 q=18481 k=1 g=13 h=0 R20=2 APRCL main test (2 59) done: p=3 q=23761 k=3 g=7 h=25 R20=47551980202024209520 APRCL main test (2 61) done: p=3 q=151 k=1 g=6 h=2 R20=41414141414141414138 APRCL main test (2 63) done: p=3 q=601 k=1 g=7 h=2 R20=41414141414141414138 APRCL main test (2 65) done: p=3 q=1051 k=1 g=7 h=0 R20=2 APRCL main test (2 66) done: p=3 q=1201 k=1 g=11 h=2 R20=41414141414141414138 APRCL main test (2 67) done: p=3 q=1801 k=2 g=11 h=8 R20=57599375976729563628 APRCL main test (2 69) done: p=3 q=3301 k=1 g=6 h=2 R20=41414141414141414138 APRCL main test (2 71) done: p=3 q=4201 k=1 g=11 h=1 R20=1 APRCL main test (2 72) done: p=3 q=4951 k=2 g=6 h=0 R20=2379496310429498542 APRCL main test (2 73) done: p=3 q=6301 k=2 g=10 h=8 R20=63218820815600928864 APRCL main test (2 74) done: p=3 q=9901 k=2 g=2 h=5 R20=74638128510526523885 APRCL main test (2 75) done: p=3 q=11551 k=1 g=7 h=0 R20=2 APRCL main test (2 76) done: p=3 q=12601 k=2 g=11 h=2 R20=45386810327803273305 APRCL main test (2 77) done: p=3 q=14851 k=3 g=2 h=8 R20=88550916096664723267 APRCL main test (2 79) done: p=3 q=19801 k=2 g=13 h=2 R20=30180052961439194453 APRCL main test (2 80) done: p=3 q=97 k=1 g=5 h=0 R20=2 APRCL main test (2 82) done: p=3 q=673 k=1 g=5 h=0 R20=2 APRCL main test (2 83) done: p=3 q=2017 k=2 g=5 h=7 R20=6243825219283446355 APRCL main test (2 84) done: p=3 q=3169 k=2 g=7 h=7 R20=55036988031467244787 APRCL main test (2 85) done: p=3 q=3361 k=1 g=22 h=0 R20=2 APRCL main test (2 86) done: p=3 q=5281 k=1 g=7 h=1 R20=1 APRCL main test (2 87) done: p=3 q=7393 k=1 g=5 h=2 R20=41414141414141414138 APRCL main test (2 88) done: p=3 q=21601 k=3 g=7 h=23 R20=30027897281233378871 APRCL main test (2 89) done: p=3 q=30241 k=3 g=11 h=19 R20=88753962303467317050 APRCL main test (2 91) done: p=3 q=79 k=1 g=3 h=2 R20=41414141414141414138 APRCL main test (2 93) done: p=3 q=157 k=1 g=5 h=1 R20=1 APRCL main test (2 94) done: p=3 q=313 k=1 g=10 h=2 R20=41414141414141414138 APRCL main test (2 96) done: p=3 q=547 k=1 g=2 h=1 R20=1 APRCL main test (2 97) done: p=3 q=859 k=1 g=2 h=2 R20=41414141414141414138 APRCL main test (2 99) done: p=3 q=937 k=2 g=5 h=4 R20=62624565354071982738 APRCL main test (2 100) done: p=3 q=1093 k=1 g=5 h=2 R20=41414141414141414138 APRCL main test (2 101) done: p=3 q=1171 k=2 g=2 h=1 R20=49502452127596964482 APRCL main test (2 102) done: p=3 q=1249 k=1 g=7 h=1 R20=1 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=1 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=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=4 R20=41414141414141414134 APRCL main test (3 16) done: p=5 q=211 k=1 g=2 h=0 R20=4 APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=2 R20=1 APRCL main test (3 18) done: p=5 q=631 k=1 g=3 h=2 R20=1 APRCL main test (3 19) done: p=5 q=41 k=1 g=6 h=4 R20=41414141414141414134 APRCL main test (3 21) done: p=5 q=281 k=1 g=3 h=3 R20=1 APRCL main test (3 22) done: p=5 q=2521 k=1 g=17 h=3 R20=1 APRCL main test (3 25) done: p=5 q=241 k=1 g=7 h=4 R20=41414141414141414134 APRCL main test (3 29) done: p=5 q=271 k=1 g=6 h=1 R20=1 APRCL main test (3 32) done: p=5 q=541 k=1 g=2 h=2 R20=1 APRCL main test (3 34) done: p=5 q=2161 k=1 g=23 h=0 R20=4 APRCL main test (3 35) done: p=5 q=7561 k=1 g=13 h=1 R20=1 APRCL main test (3 36) done: p=5 q=15121 k=1 g=11 h=4 R20=41414141414141414134 APRCL main test (3 41) done: p=5 q=331 k=1 g=3 h=0 R20=4 APRCL main test (3 45) done: p=5 q=661 k=1 g=2 h=0 R20=4 APRCL main test (3 46) done: p=5 q=881 k=1 g=3 h=1 R20=1 APRCL main test (3 47) done: p=5 q=991 k=1 g=6 h=3 R20=1 APRCL main test (3 48) done: p=5 q=1321 k=1 g=13 h=3 R20=1 APRCL main test (3 49) done: p=5 q=2311 k=1 g=3 h=2 R20=1 APRCL main test (3 51) done: p=5 q=2971 k=1 g=10 h=4 R20=41414141414141414134 APRCL main test (3 54) done: p=5 q=4621 k=1 g=2 h=0 R20=4 APRCL main test (3 56) done: p=5 q=9241 k=1 g=13 h=0 R20=4 APRCL main test (3 58) done: p=5 q=18481 k=1 g=13 h=3 R20=1 APRCL main test (3 59) done: p=5 q=23761 k=1 g=7 h=2 R20=1 APRCL main test (3 60) done: p=5 q=101 k=2 g=2 h=23 R20=83979557203867690758 APRCL main test (3 61) done: p=5 q=151 k=2 g=6 h=20 R20=81618028954264819458 APRCL main test (3 62) done: p=5 q=401 k=2 g=3 h=8 R20=52905652267561275102 APRCL main test (3 63) done: p=5 q=601 k=2 g=7 h=9 R20=72319036124994569084 APRCL main test (3 64) done: p=5 q=701 k=2 g=2 h=24 R20=97906673031466999649 APRCL main test (3 65) done: p=5 q=1051 k=2 g=7 h=22 R20=23934945132173717454 APRCL main test (3 66) done: p=5 q=1201 k=2 g=11 h=1 R20=42240597772805062913 APRCL main test (3 67) done: p=5 q=1801 k=2 g=11 h=20 R20=20030990364527368055 APRCL main test (3 68) done: p=5 q=2801 k=2 g=3 h=22 R20=52366667846324511025 APRCL main test (3 69) done: p=5 q=3301 k=2 g=6 h=2 R20=31907951905408866691 APRCL main test (3 70) done: p=5 q=3851 k=2 g=2 h=22 R20=68705426349964587120 APRCL main test (3 71) done: p=5 q=4201 k=2 g=11 h=17 R20=57912783850008315415 APRCL main test (3 72) done: p=5 q=4951 k=2 g=6 h=11 R20=60601196962765509764 APRCL main test (3 73) done: p=5 q=6301 k=2 g=10 h=11 R20=260289928196679327 APRCL main test (3 74) done: p=5 q=9901 k=2 g=2 h=13 R20=89436192318487795876 APRCL main test (3 75) done: p=5 q=11551 k=2 g=7 h=17 R20=66030566862646150002 Parameters saved: 2 21621600 3 76 1 1 1825 APRCL main test (3 76) done: p=5 q=12601 k=2 g=11 h=3 R20=42274455034096832733 APRCL main test (3 77) done: p=5 q=14851 k=2 g=2 h=16 R20=66028272469642616686 APRCL main test (3 78) done: p=5 q=15401 k=2 g=6 h=8 R20=67968359351442059594 APRCL main test (3 79) done: p=5 q=19801 k=2 g=13 h=21 R20=51809965907526737607 APRCL main test (3 85) done: p=5 q=3361 k=1 g=22 h=3 R20=1 APRCL main test (3 86) done: p=5 q=5281 k=1 g=7 h=2 R20=1 APRCL main test (3 88) done: p=5 q=21601 k=2 g=7 h=4 R20=68524051941341948647 APRCL main test (3 89) done: p=5 q=30241 k=1 g=11 h=1 R20=1 APRCL main test (3 92) done: p=5 q=131 k=1 g=2 h=3 R20=1 APRCL main test (3 95) done: p=5 q=521 k=1 g=3 h=1 R20=1 APRCL main test (3 98) done: p=5 q=911 k=1 g=17 h=2 R20=1 APRCL main test (3 101) done: p=5 q=1171 k=1 g=2 h=3 R20=1 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=1 APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=2 R20=1 APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=4 R20=1 APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=3 R20=1 APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=2 R20=1 APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=6 R20=41414141414141414130 APRCL main test (4 18) done: p=7 q=631 k=1 g=3 h=0 R20=6 APRCL main test (4 21) done: p=7 q=281 k=1 g=3 h=6 R20=41414141414141414130 APRCL main test (4 22) done: p=7 q=2521 k=1 g=17 h=0 R20=6 APRCL main test (4 24) done: p=7 q=113 k=1 g=3 h=4 R20=1 APRCL main test (4 26) done: p=7 q=337 k=1 g=10 h=5 R20=1 APRCL main test (4 27) done: p=7 q=1009 k=1 g=11 h=6 R20=41414141414141414130 APRCL main test (4 30) done: p=7 q=379 k=1 g=2 h=1 R20=1 APRCL main test (4 33) done: p=7 q=757 k=1 g=2 h=5 R20=1 APRCL main test (4 35) done: p=7 q=7561 k=1 g=13 h=6 R20=41414141414141414130 APRCL main test (4 36) done: p=7 q=15121 k=1 g=11 h=1 R20=1 APRCL main test (4 43) done: p=7 q=463 k=1 g=3 h=6 R20=41414141414141414130 APRCL main test (4 44) done: p=7 q=617 k=1 g=3 h=0 R20=6 APRCL main test (4 49) done: p=7 q=2311 k=1 g=3 h=4 R20=1 APRCL main test (4 52) done: p=7 q=3697 k=1 g=5 h=5 R20=1 APRCL main test (4 53) done: p=7 q=4159 k=1 g=3 h=4 R20=1 APRCL main test (4 54) done: p=7 q=4621 k=1 g=2 h=4 R20=1 APRCL main test (4 55) done: p=7 q=8317 k=1 g=6 h=3 R20=1 APRCL main test (4 56) done: p=7 q=9241 k=1 g=13 h=2 R20=1 APRCL main test (4 57) done: p=7 q=16633 k=1 g=15 h=5 R20=1 APRCL main test (4 58) done: p=7 q=18481 k=1 g=13 h=5 R20=1 APRCL main test (4 64) done: p=7 q=701 k=1 g=2 h=1 R20=1 APRCL main test (4 65) done: p=7 q=1051 k=1 g=7 h=6 R20=41414141414141414130 APRCL main test (4 68) done: p=7 q=2801 k=1 g=3 h=1 R20=1 APRCL main test (4 70) done: p=7 q=3851 k=1 g=2 h=0 R20=6 APRCL main test (4 71) done: p=7 q=4201 k=1 g=11 h=0 R20=6 APRCL main test (4 73) done: p=7 q=6301 k=1 g=10 h=5 R20=1 APRCL main test (4 75) done: p=7 q=11551 k=1 g=7 h=4 R20=1 APRCL main test (4 76) done: p=7 q=12601 k=1 g=11 h=0 R20=6 APRCL main test (4 78) done: p=7 q=15401 k=1 g=6 h=3 R20=1 APRCL main test (4 82) done: p=7 q=673 k=1 g=5 h=5 R20=1 APRCL main test (4 83) done: p=7 q=2017 k=1 g=5 h=2 R20=1 APRCL main test (4 85) done: p=7 q=3361 k=1 g=22 h=1 R20=1 APRCL main test (4 87) done: p=7 q=7393 k=1 g=5 h=1 R20=1 APRCL main test (4 89) done: p=7 q=30241 k=1 g=11 h=3 R20=1 APRCL main test (4 96) done: p=7 q=547 k=1 g=2 h=0 R20=6 APRCL main test (4 98) done: p=7 q=911 k=1 g=17 h=3 R20=1 APRCL main test (4 100) done: p=7 q=1093 k=1 g=5 h=0 R20=6 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=5 R20=67266790595862917532 APRCL main test (5 38) done: p=11 q=67 k=1 g=2 h=6 R20=10100625401690773192 APRCL main test (5 39) done: p=11 q=89 k=1 g=3 h=9 R20=18238066207634910415 APRCL main test (5 40) done: p=11 q=199 k=1 g=3 h=8 R20=92123547398059249737 APRCL main test (5 41) done: p=11 q=331 k=1 g=3 h=9 R20=85734326193983385889 APRCL main test (5 42) done: p=11 q=397 k=1 g=5 h=8 R20=14232179040501298390 APRCL main test (5 43) done: p=11 q=463 k=1 g=3 h=10 R20=25491489048091897949 APRCL main test (5 44) done: p=11 q=617 k=1 g=3 h=5 R20=30529472881004066985 APRCL main test (5 45) done: p=11 q=661 k=1 g=2 h=1 R20=89848120539808951893 APRCL main test (5 46) done: p=11 q=881 k=1 g=3 h=4 R20=7422205695988469047 APRCL main test (5 47) done: p=11 q=991 k=1 g=6 h=9 R20=40297480314787153367 APRCL main test (5 48) done: p=11 q=1321 k=1 g=13 h=5 R20=5407295036188124843 APRCL main test (5 49) done: p=11 q=2311 k=1 g=3 h=9 R20=98325245110302840489 APRCL main test (5 50) done: p=11 q=2377 k=1 g=5 h=6 R20=98877687725372029434 APRCL main test (5 51) done: p=11 q=2971 k=1 g=10 h=0 R20=26603930303744153976 APRCL main test (5 52) done: p=11 q=3697 k=1 g=5 h=2 R20=34641359978452725064 APRCL main test (5 53) done: p=11 q=4159 k=1 g=3 h=8 R20=58688912192985186641 APRCL main test (5 54) done: p=11 q=4621 k=1 g=2 h=7 R20=67486576631971120718 APRCL main test (5 55) done: p=11 q=8317 k=1 g=6 h=5 R20=33988934327827832697 APRCL main test (5 56) done: p=11 q=9241 k=1 g=13 h=6 R20=53237348565316850474 APRCL main test (5 57) done: p=11 q=16633 k=1 g=15 h=5 R20=76776920961224007453 APRCL main test (5 58) done: p=11 q=18481 k=1 g=13 h=8 R20=60824098699358338407 APRCL main test (5 59) done: p=11 q=23761 k=1 g=7 h=9 R20=24527445739606490674 APRCL main test (5 69) done: p=11 q=3301 k=1 g=6 h=9 R20=89793404377979964208 APRCL main test (5 70) done: p=11 q=3851 k=1 g=2 h=4 R20=54822617536947355295 APRCL main test (5 72) done: p=11 q=4951 k=1 g=6 h=7 R20=40364254870589793475 APRCL main test (5 74) done: p=11 q=9901 k=1 g=2 h=8 R20=57761640994244135171 APRCL main test (5 75) done: p=11 q=11551 k=1 g=7 h=7 R20=94750055201377216552 APRCL main test (5 77) done: p=11 q=14851 k=1 g=2 h=6 R20=78168721181905353288 APRCL main test (5 78) done: p=11 q=15401 k=1 g=6 h=3 R20=15908178076860202479 APRCL main test (5 79) done: p=11 q=19801 k=1 g=13 h=2 R20=16159583633862085373 APRCL main test (5 81) done: p=11 q=353 k=1 g=3 h=4 R20=99762582052926981020 APRCL main test (5 84) done: p=11 q=3169 k=1 g=7 h=0 R20=38943493197050339206 APRCL main test (5 86) done: p=11 q=5281 k=1 g=7 h=8 R20=87482456081394002946 APRCL main test (5 87) done: p=11 q=7393 k=1 g=5 h=4 R20=73628348097663943015 APRCL main test (5 97) done: p=11 q=859 k=1 g=2 h=10 R20=83630109312308709442 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=1 R20=1 APRCL main test (6 91) done: p=13 q=79 k=1 g=3 h=0 R20=12 APRCL main test (6 92) done: p=13 q=131 k=1 g=2 h=9 R20=1 APRCL main test (6 93) done: p=13 q=157 k=1 g=5 h=4 R20=1 APRCL main test (6 94) done: p=13 q=313 k=1 g=10 h=0 R20=12 APRCL main test (6 95) done: p=13 q=521 k=1 g=3 h=5 R20=1 APRCL main test (6 96) done: p=13 q=547 k=1 g=2 h=4 R20=1 APRCL main test (6 97) done: p=13 q=859 k=1 g=2 h=8 R20=1 APRCL main test (6 98) done: p=13 q=911 k=1 g=17 h=6 R20=1 APRCL main test (6 99) done: p=13 q=937 k=1 g=5 h=0 R20=12 APRCL main test (6 100) done: p=13 q=1093 k=1 g=5 h=2 R20=1 APRCL main test (6 101) done: p=13 q=1171 k=1 g=2 h=6 R20=1 APRCL main test (6 102) done: p=13 q=1249 k=1 g=7 h=11 R20=1 APRCL tests for p=13 completed Main divisor test: F1=0.0234 F2=0.0000 G=0.5026 S=0.4791 T=21621600 G=37318181660361143713415702061238602127486344836031122273173089855290614175574054878145057597994673751531504988715408501070006337828003714830462003539412218456101216220079112174563596253838641316954770150754342758511435893083983142893887404601776476770911354960102369561993182979726402557724460 Parameters saved: 4 21621600 18853202 0 0 2 1801 Main divisor test passed: 21621600/21621600 *** N is prime! Time: 3769 sec
(14*10^1631-41)/99 == BPI:B263201C4DAFA ============================================ TITANIX 2.1.0 - Primality Certificate Started 07.08.2001 at 08:14:38 AM Running time 20h 10mn 21s Candidate certified prime ================================================================= Proved prime with Titanix by Hans Rosenthal. The zipped file "141_815.zip" is 262 KB. When unpacked the file "Titanix-B263201C4DAFA-001.out" is 616 KB and is available on demand by simple email request.
(14*10^6343-41)/99 Proved prime by David Broadhurst dd. December 22, 2002. Announced at http://groups.yahoo.com/group/primeform/message/2937 Details of the proof that this SUPP is prime can be found in http://groups.yahoo.com/group/primeform/files/KP/hd6342kp.txt
Thanks to Jim Fougeron for showing the way, with his BLS verification of the primality of (17*10^4885-71)/99 first proven by Hans Rosenthal and Marcel Martin, using the ECPP implementation Primo. Also thanks to OpenPfgw and Marcel Martin for their contributions to steps 1 and 2 of the present proof. Step 3 was the use of the Konyagin-Pomerance cubic given in Theorem 4.1.6 of the Crandall-Pomerance book, "Prime Numbers: A Computational Perspective". The method used depends crucially on the first (and hence last) digit being unity. Moreover one needs a good spectrum of divisors of (exponent-1): print(divisors(6342)) [1, 2, 3, 6, 7, 14, 21, 42, 151, 302, 453, 906, 1057, 2114, 3171, 6342] And then a lot of factoring work on the corresponding cyclotomic decomposition is needed (and good luck too!).
David Broadhurst

PFGW 1.1 test for probable primality in basis 3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61, and 251 made by Hans Rosenthal (Jun 04 2001) (14*10^6343-41)/99 is 3-PRP! (8.070000 seconds) (14*10^6343-41)/99 is 5-PRP! (8.020000 seconds) (14*10^6343-41)/99 is 7-PRP! (8.020000 seconds) (14*10^6343-41)/99 is 11-PRP! (8.020000 seconds) (14*10^6343-41)/99 is 13-PRP! (8.020000 seconds) (14*10^6343-41)/99 is 17-PRP! (8.020000 seconds) (14*10^6343-41)/99 is 19-PRP! (8.020000 seconds) (14*10^6343-41)/99 is 23-PRP! (8.020000 seconds) (14*10^6343-41)/99 is 29-PRP! (8.080000 seconds) (14*10^6343-41)/99 is 31-PRP! (8.020000 seconds) (14*10^6343-41)/99 is 37-PRP! (8.020000 seconds) (14*10^6343-41)/99 is 41-PRP! (8.020000 seconds) (14*10^6343-41)/99 is 43-PRP! (8.020000 seconds) (14*10^6343-41)/99 is 47-PRP! (8.080000 seconds) (14*10^6343-41)/99 is 53-PRP! (8.020000 seconds) (14*10^6343-41)/99 is 59-PRP! (8.020000 seconds) (14*10^6343-41)/99 is 61-PRP! (8.020000 seconds) (14*10^6343-41)/99 is 251-PRP! (8.020000 seconds)
(14*10^14689-41)/99 PFGW 1.1 test for probable primality in basis 3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61, and 251 (14*10^14689-41)/99 is 3-PRP! (55.360000 seconds) (14*10^14689-41)/99 is 5-PRP! (54.820000 seconds) (14*10^14689-41)/99 is 7-PRP! (54.760000 seconds) (14*10^14689-41)/99 is 11-PRP! (54.870000 seconds) (14*10^14689-41)/99 is 13-PRP! (54.870000 seconds) (14*10^14689-41)/99 is 17-PRP! (54.870000 seconds) (14*10^14689-41)/99 is 19-PRP! (54.760000 seconds) (14*10^14689-41)/99 is 23-PRP! (54.820000 seconds) (14*10^14689-41)/99 is 29-PRP! (54.810000 seconds) (14*10^14689-41)/99 is 31-PRP! (54.760000 seconds) (14*10^14689-41)/99 is 37-PRP! (54.870000 seconds) (14*10^14689-41)/99 is 41-PRP! (54.920000 seconds) (14*10^14689-41)/99 is 43-PRP! (54.810000 seconds) (14*10^14689-41)/99 is 47-PRP! (54.810000 seconds) (14*10^14689-41)/99 is 53-PRP! (54.820000 seconds) (14*10^14689-41)/99 is 59-PRP! (54.810000 seconds) (14*10^14689-41)/99 is 61-PRP! (54.820000 seconds) (14*10^14689-41)/99 is 251-PRP! (54.760000 seconds)