Smoothly Undulating Palindromic Primes





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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)