(10^3-1)/9 + 4*10^1
*** 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



(10^15-1)/9 + 4*10^7
== ID:B2813039515A2 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 111111151111111

Decimal size = 15
Binary size = 47

-----------------------------------------------------------------
1) SPP Test
-----------------------------------------------------------------
N = Candidate

Started 11/01/2002 04:41:42 PM
Running time < 1s

Candidate certified prime

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

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



(10^91-1)/9 + 4*10^45
== ID:B281303930B36 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 111111111111111111111111111111111111111111111511111111111111\
    1111111111111111111111111111111

Decimal size = 91
Binary size = 300

Started 11/01/2002 04:39:28 PM
Running time < 1s

Candidate certified prime

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

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



(10^231-1)/9 + 4*10^115
== ID:B281303901642 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 111111111111111111111111111111111111111111111111111111111111\
    111111111111111111111111111111111111111111111111111111151111\
    111111111111111111111111111111111111111111111111111111111111\
    111111111111111111111111111111111111111111111111111

Decimal size = 231
Binary size = 765

Started 11/01/2002 04:36:14 PM
Running time 14s

Candidate certified prime

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

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



(10^1363-1)/9 + 4*10^681
== ID:B27F104B67408 =============================================

PRIMO 1.2.1 - Primality Certificate - (1)681 5(1)681

Started 09/28/2002 09:57:46 PM
Running time 2h 56mn 4s

Candidate certified prime

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

Proved prime with 'Primo 1.2.1' by Jeff Heleen
using a 1.33 GHz Athlon chip.
The file "Primo-B27F104B67408.out" is 422 KB
and is available on demand by simple email request.



(10^2497-1)/9 + 4*10^1248
[PRIMO - Primality Certificate]
Version=2.0.0 - beta 3 - (1)1248 5 (1)1248
Format=2
ID=B27FA017D523E
Created=10/07/2002 06:56:30 AM
TestCount=388
Status=Candidate certified prime

[Running Times]
Initialization=14.06s
1stPhase=49h 22mn 37s
2ndPhase=4h 1mn 10s
Total=53h 24mn 2s

Proved prime with 'Primo 2.0.0 - beta 3' by Jeff Heleen
using a 1.33 GHz Athlon chip.
The file "Primo-B27FA017D523E.out" is 1072 KB
and is available on demand by simple email request.



(10^4963-1)/9 + 4*10^2481
Xinyao Chen informs me (May 19,2022) that this number is
now a proven palindromic wing prime.
Proof was done by Alfred Reich on August 17, 2013.

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



(10^5379-1)/9 + 4*10^2689
Xinyao Chen informs me (May 19,2022) that this number is
now a proven palindromic wing prime.
Proof was done by Masaki UKAI on April 24, 2020.

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



(10^12397-1)/9 + 4*10^6198
3-PRP!



(10^26395-1)/9 + 4*10^13197
3-PRP!



(10^120253-1)/9 + 4*10^60126
3-PRP! found by Robert Price on October 26, 2015.

See source at
https://stdkmd.net/nrr/1/11511.htm#prime



(10^200145-1)/9 + 4*10^100072
C:\Users\Bob\Documents\IntSeq\Details\A107125>..\pfgw64 -q"(10^(2*100072+1)+36*10^100072-1)/9" -tc

PFGW Version 3.7.7.64BIT.20130722.Win_Dev [GWNUM 27.11]
Primality testing (10^(2*100072+1)+36*10^100072-1)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N+1 BLS with factored part 0.00% and helper 0.00% (0.01% proof)
(10^(2*100072+1)+36*10^100072-1)/9 is Fermat and Lucas PRP! (8733.3329s+0.0100s)

Probable Prime proved by Robert Price on September 5, 2023.
 

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Patrick De Geest - Belgium flag - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com