5*(10^3-1)/9 - 4*(10^2+1)
*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(15*10^3-51)/99
N=151
*** N is prime!
Time: 0 sec



5*(10^3-1)/9 - 4*(10^2+1)
run"aprt-cle
Test number  N=? 15551

Preparatory test
    Pass !

 15551 is prime.
  0:00:00
OK

Proved prime with 'Ubasic - APRT-CLE.UB'
by Patrick De Geest using a Pentium III 650 MHz chip.



5*(10^21-1)/9 - 4*(10^20+1)
== ID:B286400C4F9AA =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 155555555555555555551

Decimal size = 21
Binary size = 68

-----------------------------------------------------------------
1) N+1 Test
-----------------------------------------------------------------
N = Candidate
S = 608
R = 255847953216374269
Q = 3

-----------------------------------------------------------------
2) N-1 Test
-----------------------------------------------------------------
N = R of preceding test
S = 363612
R = 703629014489
B = 2

-----------------------------------------------------------------
3) SPP Test
-----------------------------------------------------------------
N = R of preceding test

Started 01/21/2003 03:35:09 AM
Running time < 1s

Candidate certified prime

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

Proved prime with 'Primo 1.2.1'
by Patrick De Geest using a Pentium III 650 MHz chip.



5*(10^33-1)/9 - 4*(10^32+1)
== ID:B286501069DA6 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 155555555555555555555555555555551

Decimal size = 33
Binary size = 107

-----------------------------------------------------------------
1) N+1 Test
-----------------------------------------------------------------
N = Candidate
S = 295648
R = 526151218866880735048285649
Q = 3

-----------------------------------------------------------------
2) EC Test
-----------------------------------------------------------------
N = R of preceding test
S = 16420
R = 32043314181907603710397
A = 2
B = 0
T = 4

-----------------------------------------------------------------
3) N-1 Test
-----------------------------------------------------------------
N = R of preceding test
S = 34884
R = 918567658006753919
B = 2

-----------------------------------------------------------------
4) N-1 Test
-----------------------------------------------------------------
N = R of preceding test
S = 17398
R = 52797313369741
B = 2

-----------------------------------------------------------------
5) SPP Test
-----------------------------------------------------------------
N = R of preceding test

Started 01/22/2003 04:46:50 AM
Running time < 1s

Candidate certified prime

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

Proved prime with 'Primo 1.2.1'
by Patrick De Geest using a Pentium III 650 MHz chip.



5*(10^401-1)/9 - 4*(10^400+1)
== ID:B286A03C9A1DC =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 155555555555555555555555555555555555555555555555555555555555\
    555555555555555555555555555555555555555555555555555555555555\
    555555555555555555555555555555555555555555555555555555555555\
    555555555555555555555555555555555555555555555555555555555555\
    555555555555555555555555555555555555555555555555555555555555\
    555555555555555555555555555555555555555555555555555555555555\
    55555555555555555555555555555555555555551

Decimal size = 401
Binary size = 1330


Started 01/27/2003 05:39:05 PM
Running time 4mn 25s

Candidate certified prime

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

Proved prime with 'Primo 1.2.1'
by Patrick De Geest using a Pentium III 650 MHz chip.



5*(10^563-1)/9 - 4*(10^562+1)
== ID:B286C03B4CFBE =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 155555555555555555555555555555555555555555555555555555555555\
    555555555555555555555555555555555555555555555555555555555555\
    555555555555555555555555555555555555555555555555555555555555\
    555555555555555555555555555555555555555555555555555555555555\
    555555555555555555555555555555555555555555555555555555555555\
    555555555555555555555555555555555555555555555555555555555555\
    555555555555555555555555555555555555555555555555555555555555\
    555555555555555555555555555555555555555555555555555555555555\
    555555555555555555555555555555555555555555555555555555555555\
    55555555555555555555551

Decimal size = 563
Binary size = 1868


Started 01/29/2003 05:16:21 PM
Running time 12mn 54s

Candidate certified prime

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

Proved prime with 'Primo 1.2.1'
by Patrick De Geest using a Pentium III 650 MHz chip.



5*(10^7017-1)/9 - 4*(10^7016+1)
Xinyao Chen informs me (May 19,2022) that this number is
now a proven palindromic plateau & depression prime.
Proof was done by Maksym Voznyy on November 13, 2020.

See source at
https://stdkmd.net/nrr/records.htm#pdprime



5*(10^37685-1)/9 - 4*(10^37684+1)
3-PRP!



5*(10^211263-1)/9 - 4*(10^211262+1)
by Serge Batalov dd. January 20, 2023.

https://stdkmd.net/nrr/1/15551.htm#prime



5*(10^222719-1)/9 - 4*(10^222718+1)
by Serge Batalov dd. January 21, 2023.

https://stdkmd.net/nrr/1/15551.htm#prime



5*(10^250337-1)/9 - 4*(10^250336+1)
by Serge Batalov dd. January 22, 2023.

https://stdkmd.net/nrr/1/15551.htm#prime

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( © All rights reserved ) - Last modified : March 15, 2023.
Patrick De Geest - Belgium flag - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com