*** 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

== ID:B280C00F5A82A =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 99999199999

Decimal size = 11
Binary size = 37

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

Started 10/25/2002 04:28:19 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.

== ID:B280C00F2CA6A =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 999999999999919999999999999

Decimal size = 27
Binary size = 90

Started 10/25/2002 04:25:11 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.

== ID:B280C00EEDDD8 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 999999999999999999999999999999999999999999919999999999999999\
    999999999999999999999999999

Decimal size = 87
Binary size = 290

Started 10/25/2002 04:20:54 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.

== ID:B280C00EA709A =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999919999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999

Decimal size = 339
Binary size = 1127

Started 10/25/2002 04:16:04 AM
Running time 1mn 3s

Candidate certified prime

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

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

== ID:B280B00D40AE4 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    919999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999999999999999999999999999999999999999999999999999999999999\
    999

Decimal size = 363
Binary size = 1206

Started 10/24/2002 03:51:36 AM
Running time 1mn 12s

Candidate certified prime

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

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

(9)15791(9)1579 is prime, it is provable by a N+1 method.

C:\PrimeForm>pfgw -q10^3159-8*10^1579-1 -tp
PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor')

Primality testing 10^3159-8*10^1579-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 34.94%
10^3159-8*10^1579-1 is prime! (16.040000 seconds)

(Timing using a Pentium III 650 Mhz chip).

The form of this prime is P = 10^(2n+1)-a*10^n-1 = 10^n(10^(n+1)-a)-1.
P+1 is "factorable" for 50%, so a N+1 methode is available
and PFGW (PrimeForm) can prove it.

C:\PrimeForm>pfgw -q10^36155-8*10^18077-1 -tp
PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor')

Primality testing 10^36155-8*10^18077-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 34.95%
10^36155-8*10^18077-1 is prime! (3683.970000 seconds)

(Timing using a Pentium III 650 Mhz chip).

The form of this prime is P = 10^(2n+1)-a*10^n-1 = 10^n(10^(n+1)-a)-1.
P+1 is "factorable" for 50%, so a N+1 methode is available
and PFGW (PrimeForm) can prove it.

C:\PrimeForm>pfgw -q10^45305-8*10^22652-1 -tp
PFGW Version 20010212.Win_Dev (Beta software, 'caveat utilitor')

Primality testing 10^45305-8*10^22652-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 34.95%
10^45305-8*10^22652-1 is prime! (6455.060000 seconds)

(Timing using a Pentium III 650 Mhz chip).

By Darren Bedwell

https://primes.utm.edu/primes/page.php?id=110658
http://zerosink.blogspot.com/2013/01/new-record-near-repdigit-palindromic.html
Top Twenty Palindromic Primes


Primality testing 10^(2*157363+1)-8*10^157363-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Generic modular reduction using generic reduction AMD K10 type-1 FFT length 112K, Pass1=112, Pass2=1K on A 1045501-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 34.95%
10^(2*157363+1)-8*10^157363-1 is prime! (39200.4130s+0.7439s)