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(98*10^9-89)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(98*10^9-89)/99 N=989898989 *** N is prime! Time: 0 sec
(98*10^161-89)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(98*10^161-89)/99 N=98989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989 Factor: 2^2 divides N - 1 Factor: 2 divides N + 1 Factor: 3^2 divides N - 1 Factor: 5 divides N + 1 Factor: 11 divides N - 1 Factor: 31 divides N - 1 Factor: 61^2 divides N - 1 Factor: 67^2 divides N + 1 Factor: 263 divides N - 1 Factor: 521^2 divides N + 1 Factorization results: F1=0.0626 F2=0.0626 F1=12013575948 F2=12184986490 Pass: gcd(13^((N-1)/2) - 1, N) = 1: R20=89898989898989898987 Pass: 13^(N-1) = 1 (mod N): R20=1 Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=1 q=-3 R20=0 Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=3 q=-1 R20=0 Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=5 q=3 R20=0 Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=7 q=9 R20=0 Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=9 q=17 R20=0 Fail: gcd(U{(N+1)/2}, N) not = 1: d=13 p=11 q=27 R20=0 Pass: gcd(U{(N+1)/2}, N) = 1: d=13 p=13 q=39 R20=93574178514834320829 Pass: U{N+1} = 0 (mod N): d=13 p=13 q=39 R20=0 Fail: gcd(13^((N-1)/3) - 1, N) not = 1: R20=0 Pass: gcd(19^((N-1)/3) - 1, N) = 1: R20=12641233650261334180 Pass: 19^(N-1) = 1 (mod N): R20=1 Fail: gcd(U{(N+1)/5}, N) not = 1: d=13 p=13 q=39 R20=0 Pass: gcd(U{(N+1)/5}, N) = 1: d=13 p=15 q=53 R20=39043842177902606278 Pass: U{N+1} = 0 (mod N): d=13 p=15 q=53 R20=0 Pass: gcd(19^((N-1)/11) - 1, N) = 1: R20=19412087966163075816 Pass: gcd(19^((N-1)/31) - 1, N) = 1: R20=36725962282032502602 Pass: gcd(19^((N-1)/61) - 1, N) = 1: R20=84202025410611317140 Pass: gcd(U{(N+1)/67}, N) = 1: d=13 p=15 q=53 R20=19369658788103185249 Pass: gcd(19^((N-1)/263) - 1, N) = 1: R20=96902622557537293803 Pass: gcd(U{(N+1)/521}, N) = 1: d=13 p=15 q=53 R20=4884677600579124997 BLS tests passed: F1=0.0626 F2=0.0626 APRCL test T=15120 S=73150606177799210017409845561213808454698435854035890088283201 APRCL main test (1) at level 7 for p=2 APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=0 R20=1 APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=2 R20=89898989898989898987 APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=0 R20=1 APRCL L_2 condition satisfied APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=1 R20=0 APRCL main test (1 6) for p=2 q=11 not needed APRCL main test (1 7) for p=2 q=31 not needed APRCL main test (1 8) for p=2 q=61 not needed APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=1 R20=89898989898989898988 APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=3 R20=0 APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=0 R20=2 APRCL main test (1 12) done: p=2 q=29 k=2 g=2 h=2 R20=89898989898989898987 APRCL main test (1 13) done: p=2 q=43 k=1 g=3 h=1 R20=89898989898989898988 APRCL main test (1 14) done: p=2 q=71 k=1 g=7 h=1 R20=89898989898989898988 APRCL main test (1 15) done: p=2 q=127 k=1 g=3 h=0 R20=1 APRCL main test (1 16) done: p=2 q=211 k=1 g=2 h=1 R20=89898989898989898988 APRCL main test (1 17) done: p=2 q=421 k=2 g=2 h=3 R20=0 APRCL main test (1 18) done: p=2 q=631 k=1 g=3 h=1 R20=89898989898989898988 APRCL main test (1 19) done: p=2 q=41 k=3 g=6 h=2 R20=8838955151364445710 APRCL main test (1 20) done: p=2 q=73 k=3 g=5 h=0 R20=625318499640363448 APRCL main test (1 21) done: p=2 q=281 k=3 g=3 h=7 R20=44371998142151418884 APRCL main test (1 22) done: p=2 q=2521 k=3 g=17 h=1 R20=63822903029849222811 APRCL main test (1 23) done: p=2 q=17 k=4 g=3 h=2 R20=57446729738576515223 APRCL main test (1 24) done: p=2 q=113 k=4 g=3 h=7 R20=36264649290241848332 APRCL main test (1 25) done: p=2 q=241 k=4 g=7 h=4 R20=67353720353618129667 APRCL main test (1 26) done: p=2 q=337 k=4 g=10 h=10 R20=12022549680352951599 APRCL main test (1 27) done: p=2 q=1009 k=4 g=11 h=13 R20=55341119649073350825 APRCL main test (1 28) done: p=2 q=109 k=2 g=6 h=2 R20=89898989898989898987 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=4 R20=82191915256413427542 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=3 R20=0 APRCL main test (1 34) done: p=2 q=2161 k=4 g=23 h=2 R20=65724882466223419366 APRCL tests for p=2 completed APRCL main test (2) at level 7 for p=3 APRCL L_3 condition satisfied APRCL main test (2 4) done: p=3 q=7 k=1 g=3 h=2 R20=89898989898989898986 APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=2 R20=89898989898989898986 APRCL main test (2 7) for p=3 q=31 not needed APRCL main test (2 8) for p=3 q=61 not needed APRCL main test (2 9) done: p=3 q=19 k=2 g=2 h=7 R20=0 APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=6 R20=89898989898989898982 APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=3 R20=1 APRCL main test (2 13) done: p=3 q=43 k=1 g=3 h=1 R20=1 APRCL main test (2 15) done: p=3 q=127 k=2 g=3 h=6 R20=89898989898989898982 APRCL main test (2 16) done: p=3 q=211 k=1 g=2 h=2 R20=89898989898989898986 APRCL main test (2 17) done: p=3 q=421 k=1 g=2 h=1 R20=1 APRCL main test (2 18) done: p=3 q=631 k=2 g=3 h=7 R20=0 APRCL main test (2 20) done: p=3 q=73 k=2 g=5 h=3 R20=1 APRCL main test (2 22) done: p=3 q=2521 k=2 g=17 h=2 R20=0 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=1 R20=1 APRCL main test (2 27) done: p=3 q=1009 k=2 g=11 h=8 R20=0 APRCL main test (2 28) done: p=3 q=109 k=3 g=6 h=14 R20=37924007009336517713 APRCL main test (2 29) done: p=3 q=271 k=3 g=6 h=18 R20=62982943256561271631 APRCL main test (2 30) done: p=3 q=379 k=3 g=2 h=7 R20=30195563817036473730 APRCL main test (2 31) done: p=3 q=433 k=3 g=5 h=6 R20=8989927982532525245 APRCL main test (2 32) done: p=3 q=541 k=3 g=2 h=5 R20=2829268404903633843 APRCL main test (2 33) done: p=3 q=757 k=3 g=2 h=19 R20=78057795541756914193 APRCL main test (2 34) done: p=3 q=2161 k=3 g=23 h=21 R20=84196216336316093471 APRCL tests for p=3 completed APRCL main test (3) at level 7 for p=5 APRCL L_5 condition satisfied APRCL main test (3 6) for p=5 q=11 not needed APRCL main test (3 7) for p=5 q=31 not needed APRCL main test (3 8) for p=5 q=61 not needed APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=0 R20=29896539260566596255 APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=2 R20=87597768158095601743 APRCL main test (3 16) done: p=5 q=211 k=1 g=2 h=1 R20=76488644518977351633 APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=4 R20=71548840886400659862 APRCL main test (3 18) done: p=5 q=631 k=1 g=3 h=0 R20=20765516535188493551 APRCL main test (3 19) done: p=5 q=41 k=1 g=6 h=0 R20=88585182262433944456 APRCL main test (3 21) done: p=5 q=281 k=1 g=3 h=4 R20=39405376503387472476 APRCL main test (3 22) done: p=5 q=2521 k=1 g=17 h=0 R20=33893094014342355005 APRCL main test (3 25) done: p=5 q=241 k=1 g=7 h=3 R20=9972745458966368573 APRCL main test (3 29) done: p=5 q=271 k=1 g=6 h=4 R20=58785381368920327964 APRCL main test (3 32) done: p=5 q=541 k=1 g=2 h=4 R20=64440552501043864477 APRCL main test (3 34) done: p=5 q=2161 k=1 g=23 h=4 R20=10313427134229200101 APRCL tests for p=5 completed APRCL main test (4) at level 7 for p=7 APRCL L_7 condition satisfied APRCL main test (4 12) done: p=7 q=29 k=1 g=2 h=1 R20=94565193531940836053 APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=4 R20=61296337162613088003 APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=1 R20=19218004904949424676 APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=3 R20=70311447979930875951 APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=3 R20=45491777853405802344 APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=2 R20=28483630027743889861 APRCL main test (4 18) done: p=7 q=631 k=1 g=3 h=4 R20=52641671733009530960 APRCL main test (4 21) done: p=7 q=281 k=1 g=3 h=0 R20=29780479584484363455 APRCL main test (4 22) done: p=7 q=2521 k=1 g=17 h=5 R20=33004053067578104340 APRCL main test (4 24) done: p=7 q=113 k=1 g=3 h=5 R20=96657510073921640374 APRCL main test (4 26) done: p=7 q=337 k=1 g=10 h=0 R20=70218620494371496657 APRCL main test (4 27) done: p=7 q=1009 k=1 g=11 h=5 R20=23481253973105824556 APRCL main test (4 30) done: p=7 q=379 k=1 g=2 h=1 R20=69188358164394673179 APRCL main test (4 33) done: p=7 q=757 k=1 g=2 h=4 R20=45786159478752636371 APRCL tests for p=7 completed Main divisor test: F1=0.0626 F2=0.0608 G=0.5076 S=0.3843 T=15120 G=5354085275032649680736848867237665772468555467365842864695775427220997584625303260 Main divisor test passed: 15120/15120 *** N is prime! Time: 15 sec
(98*10^219-89)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(98*10^219-89)/99 N=989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989898989 Factor: 2^2 divides N - 1 Factor: 2 divides N + 1 Factor: 3^2 divides N + 1 Factor: 5 divides N + 1 Factor: 13^2 divides N - 1 Factor: 19^3 divides N - 1 Factor: 859 divides N - 1 Factorization results: F1=0.0438 F2=0.0089 F1=3982911556 F2=90 Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=89898989898989898987 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=68415288571507692006 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=78899911845577121638 Fail: gcd(U{(N+1)/5}, N) not = 1: d=17 p=3 q=-2 R20=0 Pass: gcd(U{(N+1)/5}, N) = 1: d=17 p=5 q=2 R20=4216056221314334617 Pass: U{N+1} = 0 (mod N): d=17 p=5 q=2 R20=0 Pass: gcd(3^((N-1)/13) - 1, N) = 1: R20=51706157461586583571 Pass: gcd(3^((N-1)/19) - 1, N) = 1: R20=22819491378892494087 Pass: gcd(3^((N-1)/859) - 1, N) = 1: R20=1478107705244293846 BLS tests passed: F1=0.0438 F2=0.0089 APRCL test T=166320 S=4580775695845765350176891041629641605622995896626380780137199304848580844070591186846902463546408021 APRCL main test (1) at level 8 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=89898989898989898988 APRCL main test (1 3) for p=2 q=5 not needed APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=0 R20=1 APRCL main test (1 5) for p=2 q=13 not needed APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=89898989898989898988 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=2 R20=89898989898989898987 APRCL main test (1 9) for p=2 q=19 not needed APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=2 R20=89898989898989898987 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=2 R20=89898989898989898987 APRCL main test (1 13) done: p=2 q=43 k=1 g=3 h=0 R20=1 APRCL main test (1 14) done: p=2 q=71 k=1 g=7 h=0 R20=1 APRCL main test (1 15) done: p=2 q=127 k=1 g=3 h=1 R20=89898989898989898988 APRCL main test (1 16) done: p=2 q=211 k=1 g=2 h=1 R20=89898989898989898988 APRCL main test (1 17) done: p=2 q=421 k=2 g=2 h=2 R20=89898989898989898987 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=6 R20=17914269980562918996 APRCL main test (1 20) done: p=2 q=73 k=3 g=5 h=5 R20=99483126366164650120 APRCL main test (1 21) done: p=2 q=281 k=3 g=3 h=7 R20=36670657622538125638 APRCL main test (1 22) done: p=2 q=2521 k=3 g=17 h=1 R20=55335376455493501971 APRCL main test (1 23) done: p=2 q=17 k=4 g=3 h=3 R20=27920178707029551744 APRCL main test (1 24) done: p=2 q=113 k=4 g=3 h=3 R20=13134434295475556465 APRCL main test (1 25) done: p=2 q=241 k=4 g=7 h=13 R20=97997669833236498633 APRCL main test (1 26) done: p=2 q=337 k=4 g=10 h=14 R20=60672822766334898881 APRCL main test (1 27) done: p=2 q=1009 k=4 g=11 h=10 R20=41061980476438478783 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=1 R20=89898989898989898988 APRCL main test (1 30) done: p=2 q=379 k=1 g=2 h=1 R20=89898989898989898988 APRCL main test (1 31) done: p=2 q=433 k=4 g=5 h=9 R20=40669651133826114959 APRCL main test (1 32) done: p=2 q=541 k=2 g=2 h=3 R20=0 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=6 R20=77556968678205401537 APRCL main test (1 35) done: p=2 q=7561 k=3 g=13 h=7 R20=82590797952324463122 APRCL main test (1 36) done: p=2 q=15121 k=4 g=11 h=10 R20=14802079587119451655 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=1 R20=89898989898989898988 APRCL main test (1 39) done: p=2 q=89 k=3 g=3 h=2 R20=71746138621379816542 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=89898989898989898988 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=1 R20=89898989898989898988 APRCL main test (1 44) done: p=2 q=617 k=3 g=3 h=6 R20=75873591498446504525 APRCL main test (1 45) done: p=2 q=661 k=2 g=2 h=2 R20=89898989898989898987 APRCL main test (1 46) done: p=2 q=881 k=4 g=3 h=2 R20=30838878585475159392 APRCL main test (1 47) done: p=2 q=991 k=1 g=6 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) done: p=3 q=7 k=1 g=3 h=1 R20=24242424242424242425 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=16357119582926034538 APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=1 R20=14687862228845835403 APRCL main test (2 9) for p=3 q=19 not needed APRCL main test (2 10) done: p=3 q=37 k=2 g=2 h=3 R20=66802401118998198092 APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=0 R20=49786367890230722572 APRCL main test (2 13) done: p=3 q=43 k=1 g=3 h=2 R20=11134601832276250881 APRCL main test (2 15) done: p=3 q=127 k=2 g=3 h=7 R20=94093362822803384788 APRCL main test (2 16) done: p=3 q=211 k=1 g=2 h=2 R20=15156302360093829288 APRCL main test (2 17) done: p=3 q=421 k=1 g=2 h=2 R20=75220134840087334149 APRCL main test (2 18) done: p=3 q=631 k=2 g=3 h=5 R20=33783177475831258041 APRCL main test (2 20) done: p=3 q=73 k=2 g=5 h=8 R20=45921345145242471744 APRCL main test (2 22) done: p=3 q=2521 k=2 g=17 h=6 R20=86872236421173622510 APRCL main test (2 25) done: p=3 q=241 k=1 g=7 h=0 R20=87723710130349134498 APRCL main test (2 26) done: p=3 q=337 k=1 g=10 h=1 R20=15930821568803764649 APRCL main test (2 27) done: p=3 q=1009 k=2 g=11 h=1 R20=33076187621120249650 APRCL main test (2 28) done: p=3 q=109 k=3 g=6 h=18 R20=48057851959640369304 APRCL main test (2 29) done: p=3 q=271 k=3 g=6 h=15 R20=85034152405203042041 APRCL main test (2 30) done: p=3 q=379 k=3 g=2 h=5 R20=37417370053306548858 APRCL main test (2 31) done: p=3 q=433 k=3 g=5 h=5 R20=28511477068779315712 APRCL main test (2 32) done: p=3 q=541 k=3 g=2 h=22 R20=49068365959375330351 APRCL main test (2 33) done: p=3 q=757 k=3 g=2 h=0 R20=61661851326756249902 APRCL main test (2 34) done: p=3 q=2161 k=3 g=23 h=4 R20=91566859337666203283 APRCL main test (2 35) done: p=3 q=7561 k=3 g=13 h=20 R20=8447372245236821033 APRCL main test (2 36) done: p=3 q=15121 k=3 g=11 h=6 R20=28272394147152521973 APRCL main test (2 38) done: p=3 q=67 k=1 g=2 h=1 R20=13689130107040554801 APRCL main test (2 40) done: p=3 q=199 k=2 g=3 h=1 R20=66687424418820019068 APRCL main test (2 41) done: p=3 q=331 k=1 g=3 h=0 R20=69516921480667704232 APRCL main test (2 42) done: p=3 q=397 k=2 g=5 h=0 R20=33445597895552828009 APRCL main test (2 43) done: p=3 q=463 k=1 g=3 h=1 R20=8056810000654493095 APRCL main test (2 45) done: p=3 q=661 k=1 g=2 h=0 R20=9741897033878879567 APRCL main test (2 47) done: p=3 q=991 k=2 g=6 h=5 R20=64802357310876950422 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=3 R20=18899703582195463649 APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=2 R20=56994561101710489409 APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=2 R20=20714151519253636318 APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=4 R20=16348653276424830350 APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=0 R20=98667565418739283219 APRCL main test (3 16) done: p=5 q=211 k=1 g=2 h=1 R20=35919582522838311119 APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=2 R20=89029548153414474674 APRCL main test (3 18) done: p=5 q=631 k=1 g=3 h=4 R20=82303772355168758930 APRCL main test (3 19) done: p=5 q=41 k=1 g=6 h=0 R20=17147454492689902230 APRCL main test (3 21) done: p=5 q=281 k=1 g=3 h=2 R20=84684334287458057574 APRCL main test (3 22) done: p=5 q=2521 k=1 g=17 h=1 R20=65298096658832012071 APRCL main test (3 25) done: p=5 q=241 k=1 g=7 h=0 R20=93979991624388713551 APRCL main test (3 29) done: p=5 q=271 k=1 g=6 h=3 R20=98122540651124681207 APRCL main test (3 32) done: p=5 q=541 k=1 g=2 h=2 R20=28929117818703385585 APRCL main test (3 34) done: p=5 q=2161 k=1 g=23 h=4 R20=7805799184575839694 APRCL main test (3 35) done: p=5 q=7561 k=1 g=13 h=2 R20=62185287966572182015 APRCL main test (3 36) done: p=5 q=15121 k=1 g=11 h=2 R20=13227344437130160014 APRCL main test (3 41) done: p=5 q=331 k=1 g=3 h=1 R20=46343670166710441408 APRCL main test (3 45) done: p=5 q=661 k=1 g=2 h=4 R20=19046524351105759760 APRCL main test (3 46) done: p=5 q=881 k=1 g=3 h=2 R20=96343012306123905988 APRCL main test (3 47) done: p=5 q=991 k=1 g=6 h=2 R20=26229425204881910790 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=2 R20=9819296743729889820 APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=1 R20=12282801349172863630 APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=2 R20=63043269969293477931 APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=6 R20=79102430916227457206 APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=5 R20=36270364022228497281 APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=1 R20=38451601775527740712 APRCL main test (4 18) done: p=7 q=631 k=1 g=3 h=5 R20=6348530539367165908 APRCL main test (4 21) done: p=7 q=281 k=1 g=3 h=2 R20=91978341582360251696 APRCL main test (4 22) done: p=7 q=2521 k=1 g=17 h=6 R20=50692262154849418999 APRCL main test (4 24) done: p=7 q=113 k=1 g=3 h=3 R20=55751647448490674306 APRCL main test (4 26) done: p=7 q=337 k=1 g=10 h=0 R20=31755703673323500671 APRCL main test (4 27) done: p=7 q=1009 k=1 g=11 h=5 R20=36703139012152085718 APRCL main test (4 30) done: p=7 q=379 k=1 g=2 h=6 R20=89630833793594519685 APRCL main test (4 33) done: p=7 q=757 k=1 g=2 h=4 R20=19046787794966916169 APRCL main test (4 35) done: p=7 q=7561 k=1 g=13 h=6 R20=46992916917301437029 APRCL main test (4 36) done: p=7 q=15121 k=1 g=11 h=1 R20=10570242854671019914 APRCL main test (4 43) done: p=7 q=463 k=1 g=3 h=5 R20=30720972200780835388 APRCL main test (4 44) done: p=7 q=617 k=1 g=3 h=1 R20=5848252616876901720 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=2 R20=98807882392757939481 APRCL main test (5 38) done: p=11 q=67 k=1 g=2 h=7 R20=84038821110544851490 APRCL main test (5 39) done: p=11 q=89 k=1 g=3 h=4 R20=9108095404322552189 APRCL main test (5 40) done: p=11 q=199 k=1 g=3 h=7 R20=92359868761759464519 APRCL main test (5 41) done: p=11 q=331 k=1 g=3 h=4 R20=24210403851696645089 APRCL main test (5 42) done: p=11 q=397 k=1 g=5 h=6 R20=9157373042226372641 APRCL main test (5 43) done: p=11 q=463 k=1 g=3 h=6 R20=74759704825893707032 APRCL main test (5 44) done: p=11 q=617 k=1 g=3 h=0 R20=29757519028797803115 APRCL main test (5 45) done: p=11 q=661 k=1 g=2 h=9 R20=70877045266328627195 APRCL main test (5 46) done: p=11 q=881 k=1 g=3 h=8 R20=19772055939964001160 APRCL main test (5 47) done: p=11 q=991 k=1 g=6 h=0 R20=30325442266734979838 APRCL tests for p=11 completed Main divisor test: F1=0.0438 F2=0.0075 G=0.5065 S=0.4551 T=166320 G=821017100449261800309776668823680948042840122120620704064913586954046076332204627302992736118873576210939580420 Main divisor test passed: 166320/166320 *** N is prime! Time: 53 sec
(98*10^4859-89)/99 == ID:B268A04F8FE04 ============================================= PRIMO 1.0.0 - Primality Certificate Started 07.07.2001 at 09:04:31 PM Running time 1847h 10mn 59s Candidate certified prime ================================================================= Proved prime with 'Primo' by Hans Rosenthal. The zipped file "989_2429.zip" is 2298 KB. When unpacked the file "Primo-B268A04F8FE04-S.out" is 5197 KB and is available on demand by simple email request.
(98*10^21989-89)/99 PFGW 1.1 test for probable primality in bases 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, and 251 (98*10^21989-89)/99 is 3-PRP! (158.130000 seconds) (98*10^21989-89)/99 is 5-PRP! (161.370000 seconds) (98*10^21989-89)/99 is 7-PRP! (163.680000 seconds) (98*10^21989-89)/99 is 11-PRP! (165.210000 seconds) (98*10^21989-89)/99 is 13-PRP! (154.290000 seconds) (98*10^21989-89)/99 is 17-PRP! (153.840000 seconds) (98*10^21989-89)/99 is 19-PRP! (162.200000 seconds) (98*10^21989-89)/99 is 23-PRP! (158.520000 seconds) (98*10^21989-89)/99 is 29-PRP! (153.020000 seconds) (98*10^21989-89)/99 is 31-PRP! (166.200000 seconds) (98*10^21989-89)/99 is 37-PRP! (168.790000 seconds) (98*10^21989-89)/99 is 41-PRP! (157.910000 seconds) (98*10^21989-89)/99 is 43-PRP! (160.720000 seconds) (98*10^21989-89)/99 is 47-PRP! (166.200000 seconds) (98*10^21989-89)/99 is 53-PRP! (173.290000 seconds) (98*10^21989-89)/99 is 59-PRP! (158.950000 seconds) (98*10^21989-89)/99 is 61-PRP! (157.800000 seconds) (98*10^21989-89)/99 is 67-PRP! (150.930000 seconds) (98*10^21989-89)/99 is 71-PRP! (152.970000 seconds) (98*10^21989-89)/99 is 73-PRP! (165.600000 seconds) (98*10^21989-89)/99 is 79-PRP! (154.890000 seconds) (98*10^21989-89)/99 is 83-PRP! (155.220000 seconds) (98*10^21989-89)/99 is 89-PRP! (153.580000 seconds) (98*10^21989-89)/99 is 97-PRP! (163.730000 seconds) (98*10^21989-89)/99 is 101-PRP! (161.100000 seconds) (98*10^21989-89)/99 is 103-PRP! (163.460000 seconds) (98*10^21989-89)/99 is 107-PRP! (154.500000 seconds) (98*10^21989-89)/99 is 109-PRP! (158.790000 seconds) (98*10^21989-89)/99 is 113-PRP! (160.000000 seconds) (98*10^21989-89)/99 is 127-PRP! (151.430000 seconds) (98*10^21989-89)/99 is 251-PRP! (151.920000 seconds)
(98*10^52931-89)/99 Test by Ray Chandler PFGW Version 3.4.2.64BIT.20101019.Win_Dev [GWNUM 26.4] Primality testing (98*10^52931-89)/99 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 11 Running N+1 test using discriminant 17, base 2+sqrt(17) Calling N+1 BLS with factored part 0.02% and helper 0.02% (0.08% proof) (98*10^52931-89)/99 is Fermat and Lucas PRP! (1125.8090s+0.0014s)
(98*10^88595-89)/99 Test by Ray Chandler PFGW Version 3.4.8.64BIT.20110617.Win_Dev [GWNUM 26.6] Primality testing (98*10^88595-89)/99 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Generic modular reduction using generic reduction Core2 type-1 FFT length 40K, Pass1=32, Pass2=1280 on A 294313-bit number Running N-1 test using base 13 Generic modular reduction using generic reduction Core2 type-1 FFT length 40K, Pass1=32, Pass2=1280 on A 294313-bit number Running N+1 test using discriminant 19, base 1+sqrt(19) Generic modular reduction using generic reduction Core2 type-1 FFT length 40K, Pass1=32, Pass2=1280 on A 294313-bit number Calling N+1 BLS with factored part 0.01% and helper 0.00% (0.03% proof) (98*10^88595-89)/99 is Fermat and Lucas PRP! (3373.8508s+0.0109s)