Smoothly Undulating Palindromic Primes

(91*10^3-19)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(91*10^3-19)/99
N=919
*** N is prime!
Time: 0 sec

(91*10^9-19)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(91*10^9-19)/99
N=919191919
*** N is prime!
Time: 0 sec

(91*10^11-19)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(91*10^11-19)/99
N=91919191919
Factor: 2 divides N - 1
Factor: 2^4 divides N + 1
Factor: 3 divides N + 1
Factor: 5 divides N + 1
Factor: 43 divides N - 1
Factor: 157 divides N + 1
Factorization results: F1=0.1765 F2=0.4174
F1=86
F2=37680
Pass: gcd(7^((N-1)/2) - 1, N) = 1: R20=91919191917
Pass: 7^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/2}, N) = 1: d=17 p=1 q=-4 R20=38429075813
Pass: U{N+1} = 0 (mod N): d=17 p=1 q=-4 R20=0
Fail: gcd(U{(N+1)/3}, N) not = 1: d=17 p=1 q=-4 R20=0
Pass: gcd(U{(N+1)/3}, N) = 1: d=17 p=3 q=-2 R20=90547883614
Pass: U{N+1} = 0 (mod N): d=17 p=3 q=-2 R20=0
Pass: gcd(U{(N+1)/5}, N) = 1: d=17 p=3 q=-2 R20=24328691414
Pass: gcd(7^((N-1)/43) - 1, N) = 1: R20=64649682890
Pass: gcd(U{(N+1)/157}, N) = 1: d=17 p=3 q=-2 R20=38536716605
BLS tests passed: F1=0.1765 F2=0.4174
Main divisor test: F1=0.1490 F2=0.4174 G=0.5664 S=0.0000 T=1
G=1620240
Main divisor test passed: 1/1
*** N is prime!
Time: 0 sec

(91*10^17-19)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(91*10^17-19)/99
N=91919191919191919
Factor: 2 divides N - 1
Factor: 2^4 divides N + 1
Factor: 3^2 divides N + 1
Factor: 5 divides N + 1
Factor: 29 divides N - 1
Factor: 79 divides N + 1
Factorization results: F1=0.1040 F2=0.2803
F1=58
F2=56880
Pass: gcd(7^((N-1)/2) - 1, N) = 1: R20=91919191919191917
Pass: 7^(N-1) = 1 (mod N): R20=1
Pass: gcd(U{(N+1)/2}, N) = 1: d=21 p=1 q=-5 R20=35800430658758812
Pass: U{N+1} = 0 (mod N): d=21 p=1 q=-5 R20=0
Pass: gcd(U{(N+1)/3}, N) = 1: d=21 p=1 q=-5 R20=8999174815045168
Pass: gcd(U{(N+1)/5}, N) = 1: d=21 p=1 q=-5 R20=73943617370126866
Pass: gcd(7^((N-1)/29) - 1, N) = 1: R20=9453953799698218
Pass: gcd(U{(N+1)/79}, N) = 1: d=21 p=1 q=-5 R20=42016375063864109
BLS tests passed: F1=0.1040 F2=0.2803
Main divisor test: F1=0.0862 F2=0.2803 G=0.3665 S=0.0000 T=1
G=1649520
Main divisor test passed: 1/1
Final divisor test: F=0.2803 G=0.3665 H=0.9271 t=1 a=10
Final divisor test passed: 41/41 r=41 i=0
*** N is prime!
Time: 1 sec

(91*10^23-19)/99
*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(9110^23-19)/99 N=91919191919191919191919 Factor: 2 divides N - 1 Factor: 2^4 divides N + 1 Factor: 3 divides N + 1 Factor: 5 divides N + 1 Factor: 109 divides N + 1 Factorization results: F1=0.0131 F2=0.1924 F1=2 F2=26160 Pass: gcd(U{(N+1)/2}, N) = 1: d=21 p=1 q=-5 R20=33335715281287678973 Pass: U{N+1} = 0 (mod N): d=21 p=1 q=-5 R20=0 Fail: gcd(U{(N+1)/3}, N) not = 1: d=21 p=1 q=-5 R20=0 Pass: gcd(U{(N+1)/3}, N) = 1: d=21 p=3 q=-3 R20=9058713874085846312 Pass: U{N+1} = 0 (mod N): d=21 p=3 q=-3 R20=0 Pass: gcd(U{(N+1)/5}, N) = 1: d=21 p=3 q=-3 R20=36524269491601210054 Pass: gcd(U{(N+1)/109}, N) = 1: d=21 p=3 q=-3 R20=10141956808215736120 BLS tests passed: F1=0.0131 F2=0.1924 APRCL test T=180 S=35964929 APRCL main test (1) at level 3 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=42424242424242424242 APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=1 R20=19191919191919191918 APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=2 R20=29137529137529137529 APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=19191919191919191918 APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=1 R20=19191919191919191918 APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=2 R20=92607341895167748433 APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=1 R20=19191919191919191918 Retry APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=0 R20=8992038721768451498 Retry APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=2 R20=65283092516693444626 Retry from the beginning APRCL main test (1) at level 4 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=42424242424242424242 APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=1 R20=19191919191919191918 APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=2 R20=29137529137529137529 APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=19191919191919191918 APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=1 R20=19191919191919191918 APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=2 R20=92607341895167748433 Retry APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=1 R20=19191919191919191918 Retry APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=0 R20=8992038721768451498 Retry APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=2 R20=65283092516693444626 Retry APRCL L_2 condition satisfied APRCL main test (1 12) done: p=2 q=29 k=2 g=2 h=3 R20=98337717243781453056 APRCL tests for p=2 completed APRCL main test (2) at level 4 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=93939393939393939395 APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=1 R20=77777777777777777778 APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=1 R20=54056695992179863147 APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=0 R20=40519953634707733068 APRCL main test (2 9) for p=3 q=19 not needed APRCL main test (2 10) for p=3 q=37 not needed APRCL main test (2 11) for p=3 q=181 not needed APRCL tests for p=3 completed APRCL main test (3) at level 4 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=42384873503587451343 APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=1 R20=30364556734427080914 APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=1 R20=61770489649216293083 APRCL main test (3 11) for p=5 q=181 not needed APRCL tests for p=5 completed APRCL main test (4) at level 4 for p=7 APRCL L_7 condition satisfied APRCL main test (4 12) for p=7 q=29 not needed APRCL tests for p=7 completed Main divisor test: F1=0.0000 F2=0.1924 G=0.5025 S=0.3102 T=1260 G=346626199920 Main divisor test passed: 105/1260 ** N is prime! Time: 0 sec

(91*10^23-19)/99


*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(91*10^23-19)/99
N=91919191919191919191919
Factor: 2 divides N - 1
Factor: 2^4 divides N + 1
Factor: 3 divides N + 1
Factor: 5 divides N + 1
Factor: 109 divides N + 1
Factorization results: F1=0.0131 F2=0.1924
F1=2
F2=26160
Pass: gcd(U{(N+1)/2}, N) = 1: d=21 p=1 q=-5 R20=33335715281287678973
Pass: U{N+1} = 0 (mod N): d=21 p=1 q=-5 R20=0
Fail: gcd(U{(N+1)/3}, N) not = 1: d=21 p=1 q=-5 R20=0
Pass: gcd(U{(N+1)/3}, N) = 1: d=21 p=3 q=-3 R20=9058713874085846312
Pass: U{N+1} = 0 (mod N): d=21 p=3 q=-3 R20=0
Pass: gcd(U{(N+1)/5}, N) = 1: d=21 p=3 q=-3 R20=36524269491601210054
Pass: gcd(U{(N+1)/109}, N) = 1: d=21 p=3 q=-3 R20=10141956808215736120
BLS tests passed: F1=0.0131 F2=0.1924
APRCL test
T=180
S=35964929
APRCL main test (1) at level 3 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=42424242424242424242
APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=1 R20=19191919191919191918
APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=2 R20=29137529137529137529
APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=19191919191919191918
APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=1 R20=19191919191919191918
APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=2 R20=92607341895167748433
APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=1 R20=19191919191919191918
Retry
APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=0 R20=8992038721768451498
Retry
APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=2 R20=65283092516693444626
Retry from the beginning
APRCL main test (1) at level 4 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=42424242424242424242
APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=1 R20=19191919191919191918
APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=2 R20=29137529137529137529
APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=19191919191919191918
APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=1 R20=19191919191919191918
APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=2 R20=92607341895167748433
Retry
APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=1 R20=19191919191919191918
Retry
APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=0 R20=8992038721768451498
Retry
APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=2 R20=65283092516693444626
Retry
APRCL L_2 condition satisfied
APRCL main test (1 12) done: p=2 q=29 k=2 g=2 h=3 R20=98337717243781453056
APRCL tests for p=2 completed
APRCL main test (2) at level 4 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=93939393939393939395
APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=1 R20=77777777777777777778
APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=1 R20=54056695992179863147
APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=0 R20=40519953634707733068
APRCL main test (2 9) for p=3 q=19 not needed
APRCL main test (2 10) for p=3 q=37 not needed
APRCL main test (2 11) for p=3 q=181 not needed
APRCL tests for p=3 completed
APRCL main test (3) at level 4 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=42384873503587451343
APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=1 R20=30364556734427080914
APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=1 R20=61770489649216293083
APRCL main test (3 11) for p=5 q=181 not needed
APRCL tests for p=5 completed
APRCL main test (4) at level 4 for p=7
APRCL L_7 condition satisfied
APRCL main test (4 12) for p=7 q=29 not needed
APRCL tests for p=7 completed
Main divisor test: F1=0.0000 F2=0.1924 G=0.5025 S=0.3102 T=1260
G=346626199920
Main divisor test passed: 105/1260
*** N is prime!
Time: 0 sec

(91*10^25229-19)/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

(91*10^25229-19)/99 is 3-PRP! (215.090000 seconds)
(91*10^25229-19)/99 is 5-PRP! (218.990000 seconds)
(91*10^25229-19)/99 is 7-PRP! (210.580000 seconds)
(91*10^25229-19)/99 is 11-PRP! (211.630000 seconds)
(91*10^25229-19)/99 is 13-PRP! (209.700000 seconds)
(91*10^25229-19)/99 is 17-PRP! (215.370000 seconds)
(91*10^25229-19)/99 is 19-PRP! (206.140000 seconds)
(91*10^25229-19)/99 is 23-PRP! (213.770000 seconds)
(91*10^25229-19)/99 is 29-PRP! (217.010000 seconds)
(91*10^25229-19)/99 is 31-PRP! (207.680000 seconds)
(91*10^25229-19)/99 is 37-PRP! (211.460000 seconds)
(91*10^25229-19)/99 is 41-PRP! (220.090000 seconds)
(91*10^25229-19)/99 is 43-PRP! (217.340000 seconds)
(91*10^25229-19)/99 is 47-PRP! (210.140000 seconds)
(91*10^25229-19)/99 is 53-PRP! (219.430000 seconds)
(91*10^25229-19)/99 is 59-PRP! (207.560000 seconds)
(91*10^25229-19)/99 is 61-PRP! (210.530000 seconds)
(91*10^25229-19)/99 is 67-PRP! (207.010000 seconds)
(91*10^25229-19)/99 is 71-PRP! (208.170000 seconds)
(91*10^25229-19)/99 is 73-PRP! (209.810000 seconds)
(91*10^25229-19)/99 is 79-PRP! (209.930000 seconds)
(91*10^25229-19)/99 is 83-PRP! (214.810000 seconds)
(91*10^25229-19)/99 is 89-PRP! (207.060000 seconds)
(91*10^25229-19)/99 is 97-PRP! (213.280000 seconds)
(91*10^25229-19)/99 is 101-PRP! (209.770000 seconds)
(91*10^25229-19)/99 is 103-PRP! (205.420000 seconds)
(91*10^25229-19)/99 is 107-PRP! (212.890000 seconds)
(91*10^25229-19)/99 is 109-PRP! (216.950000 seconds)
(91*10^25229-19)/99 is 113-PRP! (208.500000 seconds)
(91*10^25229-19)/99 is 127-PRP! (214.210000 seconds)
(91*10^25229-19)/99 is 251-PRP! (215.860000 seconds)

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Patrick De Geest - Belgium

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