Smoothly Undulating Palindromic Primes

(35*10^3-53)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(35*10^3-53)/99
N=353
*** N is prime!
Time: 0 sec

(35*10^5-53)/99

*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(35*10^5-53)/99
N=35353
*** N is prime!
Time: 0 sec

(35*10^23-53)/99
*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(3510^23-53)/99 N=35353535353535353535353 Factor: 2^3 divides N - 1 Factor: 2 divides N + 1 Factor: 3^3 divides N - 1 Factor: 17 divides N + 1 Factor: 601 divides N - 1 Factorization results: F1=0.2268 F2=0.0679 F1=129816 F2=34 Pass: gcd(5^((N-1)/2) - 1, N) = 1: R20=53535353535353535351 Pass: 5^(N-1) = 1 (mod N): R20=1 Fail: gcd(U{(N+1)/2}, N) not = 1: d=5 p=1 q=-1 R20=0 Fail: gcd(U{(N+1)/2}, N) not = 1: d=5 p=3 q=1 R20=0 Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=5 q=5 R20=53535353535353535351 Pass: U{N+1} = 0 (mod N): d=5 p=5 q=5 R20=0 Pass: gcd(5^((N-1)/3) - 1, N) = 1: R20=49098136690746424901 Pass: gcd(U{(N+1)/17}, N) = 1: d=5 p=5 q=5 R20=79588073824515412227 Pass: gcd(5^((N-1)/601) - 1, N) = 1: R20=28438093057920841669 BLS tests passed: F1=0.2268 F2=0.0679 APRCL test T=60 S=775775 APRCL main test (1) at level 2 for p=2 APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=0 R20=1 APRCL L_2 condition satisfied APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=1 R20=0 APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=1 R20=53535353535353535352 APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=3 R20=0 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 tests for p=2 completed APRCL main test (2) at level 2 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=1 APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=2 R20=53535353535353535350 APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=0 R20=2 APRCL tests for p=3 completed APRCL main test (3) at level 2 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=14536044137847293369 APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=2 R20=51103156705519835324 APRCL tests for p=5 completed Main divisor test: F1=0.2268 F2=0.0546 G=0.5425 S=0.2612 T=60 G=1712036125800 Main divisor test passed: 60/60 ** N is prime! Time: 0 sec

(35*10^23-53)/99


*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(35*10^23-53)/99
N=35353535353535353535353
Factor: 2^3 divides N - 1
Factor: 2 divides N + 1
Factor: 3^3 divides N - 1
Factor: 17 divides N + 1
Factor: 601 divides N - 1
Factorization results: F1=0.2268 F2=0.0679
F1=129816
F2=34
Pass: gcd(5^((N-1)/2) - 1, N) = 1: R20=53535353535353535351
Pass: 5^(N-1) = 1 (mod N): R20=1
Fail: gcd(U{(N+1)/2}, N) not = 1: d=5 p=1 q=-1 R20=0
Fail: gcd(U{(N+1)/2}, N) not = 1: d=5 p=3 q=1 R20=0
Pass: gcd(U{(N+1)/2}, N) = 1: d=5 p=5 q=5 R20=53535353535353535351
Pass: U{N+1} = 0 (mod N): d=5 p=5 q=5 R20=0
Pass: gcd(5^((N-1)/3) - 1, N) = 1: R20=49098136690746424901
Pass: gcd(U{(N+1)/17}, N) = 1: d=5 p=5 q=5 R20=79588073824515412227
Pass: gcd(5^((N-1)/601) - 1, N) = 1: R20=28438093057920841669
BLS tests passed: F1=0.2268 F2=0.0679
APRCL test
T=60
S=775775
APRCL main test (1) at level 2 for p=2
APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=0 R20=1
APRCL L_2 condition satisfied
APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=1 R20=0
APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=1 R20=53535353535353535352
APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=3 R20=0
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 tests for p=2 completed
APRCL main test (2) at level 2 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=1
APRCL main test (2 5) done: p=3 q=13 k=1 g=2 h=2 R20=53535353535353535350
APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=0 R20=2
APRCL tests for p=3 completed
APRCL main test (3) at level 2 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=14536044137847293369
APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=2 R20=51103156705519835324
APRCL tests for p=5 completed
Main divisor test: F1=0.2268 F2=0.0546 G=0.5425 S=0.2612 T=60
G=1712036125800
Main divisor test passed: 60/60
*** N is prime!
Time: 0 sec

(35*10^2177-53)/99

== BPI:B26180050E574 ============================================

TITANIX 2.1.0 - Primality Certificate

Started 06.12.2001 at 01:28:21 AM
Running time 87h 10mn 54s

Candidate certified prime

=================================================================

Proved prime with Titanix by Hans Rosenthal.
The zipped file "353_1088.zip" is 444 KB.
When unpacked the file "Titanix-B26180050E574-001.out" is 1036 KB
and is available on demand by simple email request.

(35*10^3147-53)/99

== ID:B268903C51AE0 =============================================

PRIMO 1.0.0 - Primality Certificate

Started 09.26.2001 07:57:30 AM
Running time 217h 19mn 5s

Candidate certified prime

=================================================================

Proved prime with 'Primo' by Hans Rosenthal.
The zipped file "353_1573.zip" is 998 KB.
When unpacked the file "Primo-B268903C51AE0-S.out" is 2285 KB
and is available on demand by simple email request.

(35*10^4157-53)/99

== ID:B26EA01BBF692 =============================================

PRIMO 1.1.0 - Primality Certificate

Started 01.08.2002 08:05:20 AM
Running time 695h 4mn 35s
Started 02.06.2002 08:06:20 AM
Running time 112h 33mn 22s

Candidate certified prime

=================================================================

Proved prime with 'Primo' by Hans Rosenthal.
The zipped file "353_2078.zip" is 1554 KB.
When unpacked the file "Primo-B26EA01BBF692.out" is 3549 KB
and is available on demand by simple email request.

(35*10^22713-53)/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

(35*10^22713-53)/99 is 3-PRP! (188.730000 seconds)
(35*10^22713-53)/99 is 5-PRP! (193.660000 seconds)
(35*10^22713-53)/99 is 7-PRP! (197.510000 seconds)
(35*10^22713-53)/99 is 11-PRP! (191.250000 seconds)
(35*10^22713-53)/99 is 13-PRP! (194.110000 seconds)
(35*10^22713-53)/99 is 17-PRP! (192.960000 seconds)
(35*10^22713-53)/99 is 19-PRP! (193.060000 seconds)
(35*10^22713-53)/99 is 23-PRP! (186.800000 seconds)
(35*10^22713-53)/99 is 29-PRP! (189.170000 seconds)
(35*10^22713-53)/99 is 31-PRP! (195.920000 seconds)
(35*10^22713-53)/99 is 37-PRP! (197.130000 seconds)
(35*10^22713-53)/99 is 41-PRP! (189.330000 seconds)
(35*10^22713-53)/99 is 43-PRP! (187.020000 seconds)
(35*10^22713-53)/99 is 47-PRP! (190.590000 seconds)
(35*10^22713-53)/99 is 53-PRP! (195.260000 seconds)
(35*10^22713-53)/99 is 59-PRP! (190.480000 seconds)
(35*10^22713-53)/99 is 61-PRP! (190.700000 seconds)
(35*10^22713-53)/99 is 67-PRP! (200.910000 seconds)
(35*10^22713-53)/99 is 71-PRP! (193.500000 seconds)
(35*10^22713-53)/99 is 73-PRP! (189.820000 seconds)
(35*10^22713-53)/99 is 79-PRP! (192.960000 seconds)
(35*10^22713-53)/99 is 83-PRP! (193.450000 seconds)
(35*10^22713-53)/99 is 89-PRP! (199.600000 seconds)
(35*10^22713-53)/99 is 97-PRP! (198.610000 seconds)
(35*10^22713-53)/99 is 101-PRP! (195.970000 seconds)
(35*10^22713-53)/99 is 103-PRP! (189.110000 seconds)
(35*10^22713-53)/99 is 107-PRP! (199.440000 seconds)
(35*10^22713-53)/99 is 109-PRP! (188.950000 seconds)
(35*10^22713-53)/99 is 113-PRP! (186.970000 seconds)
(35*10^22713-53)/99 is 127-PRP! (188.500000 seconds)
(35*10^22713-53)/99 is 251-PRP! (186.520000 seconds)

(35*10^28385-53)/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

(35*10^28385-53)/99 is 3-PRP! (323.840000 seconds)
(35*10^28385-53)/99 is 5-PRP! (328.900000 seconds)
(35*10^28385-53)/99 is 7-PRP! (326.700000 seconds)
(35*10^28385-53)/99 is 11-PRP! (324.390000 seconds)
(35*10^28385-53)/99 is 13-PRP! (325.710000 seconds)
(35*10^28385-53)/99 is 17-PRP! (326.690000 seconds)
(35*10^28385-53)/99 is 19-PRP! (324.770000 seconds)
(35*10^28385-53)/99 is 23-PRP! (324.940000 seconds)
(35*10^28385-53)/99 is 29-PRP! (325.480000 seconds)
(35*10^28385-53)/99 is 31-PRP! (325.320000 seconds)
(35*10^28385-53)/99 is 37-PRP! (325.590000 seconds)
(35*10^28385-53)/99 is 41-PRP! (328.340000 seconds)
(35*10^28385-53)/99 is 43-PRP! (326.420000 seconds)
(35*10^28385-53)/99 is 47-PRP! (325.380000 seconds)
(35*10^28385-53)/99 is 53-PRP! (326.640000 seconds)
(35*10^28385-53)/99 is 59-PRP! (327.960000 seconds)
(35*10^28385-53)/99 is 61-PRP! (324.610000 seconds)
(35*10^28385-53)/99 is 67-PRP! (325.550000 seconds)
(35*10^28385-53)/99 is 71-PRP! (325.760000 seconds)
(35*10^28385-53)/99 is 73-PRP! (325.550000 seconds)
(35*10^28385-53)/99 is 79-PRP! (327.630000 seconds)
(35*10^28385-53)/99 is 83-PRP! (325.870000 seconds)
(35*10^28385-53)/99 is 89-PRP! (326.150000 seconds)
(35*10^28385-53)/99 is 97-PRP! (325.380000 seconds)
(35*10^28385-53)/99 is 101-PRP! (326.480000 seconds)
(35*10^28385-53)/99 is 103-PRP! (325.050000 seconds)
(35*10^28385-53)/99 is 107-PRP! (324.990000 seconds)
(35*10^28385-53)/99 is 109-PRP! (325.650000 seconds)
(35*10^28385-53)/99 is 113-PRP! (323.570000 seconds)
(35*10^28385-53)/99 is 127-PRP! (325.330000 seconds)
(35*10^28385-53)/99 is 251-PRP! (327.850000 seconds)

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Patrick De Geest - Belgium

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