Smoothly Undulating Palindromic Primes

(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 (broken link)

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

(14*10^14689-41)/99

By Hans Rosenthal

PFGW 1.1 test for probable primality in bases
3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61 and 251

(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)

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Patrick De Geest - Belgium

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