Smoothly Undulating Palindromic Primes

(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

By Hans Rosenthal

PFGW 1.1 test for probable primality in bases
3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,
71,73,79,83,89,97,101,103,107,109,113,127 and 251

(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)

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Patrick De Geest - Belgium

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