*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(78*10^3-87)/99
N=787
*** N is prime!
Time: 0 sec

== ID:B2814040BA51E =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 7778777

Decimal size = 7
Binary size = 23

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

Started 11/02/2002 06:51:12 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.

== ID:B2814040A4DA4 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 777777777777777777777777777777777777777877777777777777777777\
    7777777777777777777

Decimal size = 79
Binary size = 263

Started 11/02/2002 06:49:44 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.

== ID:B28140408ABAC =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 777777777777777777777777777777777777777777777777777777877777\
    7777777777777777777777777777777777777777777777777

Decimal size = 109
Binary size = 362

Started 11/02/2002 06:47:57 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.

== ID:B2814040631E2 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777877777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    7777777777777777777777777777777777777

Decimal size = 337
Binary size = 1120

Started 11/02/2002 06:45:14 PM
Running time 59s

Candidate certified prime

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

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

== ID:B280A010ADA38 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    877777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    7

Decimal size = 481
Binary size = 1598

Started 10/23/2002 04:51:28 AM
Running time 4mn 54s

Candidate certified prime

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

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

C:\pfgw>pfgw64 -q"7*(10^10657-1)/9 + 10^5328"
PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8]

7*(10^10657-1)/9 + 10^5328 is 3-PRP! (0.7118s+0.0009s)

C:\pfgw>pfgw64 -q"7*(10^12319-1)/9 + 10^6159"
PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8]

7*(10^12319-1)/9 + 10^6159 is 3-PRP! (0.8118s+0.0011s)

C:\Users\Bob\Documents\IntSeq\Details>pfgw64 -q"(7*10^(2*24675+1)+9*10^24675-7)/9" -tc
PFGW Version 3.7.7.64BIT.20130722.Win_Dev [GWNUM 27.11]
Primality testing (7*10^(2*24675+1)+9*10^24675-7)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge]            

Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.01% and helper 0.00% (0.03% proof)                              
(7*10^(2*24675+1)+9*10^24675-7)/9 is Fermat and Lucas PRP! (368.5817s+0.0021s)

pfgw64 -tc -q"(7*10^(2*52227+1)+9*10^52227-7)/9"
PFGW Version 3.7.7.64BIT.20130722.Win_Dev [GWNUM 27.11]
Primality testing (7*10^(2*52227+1)+9*10^52227-7)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge]            

Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.00% and helper 0.00% (0.01% proof)
(7*10^(2*52227+1)+9*10^52227-7)/9 is Fermat and Lucas PRP! (1614.9178s+0.0114s)

Found by Robert Price

(7*10^(2*113887+1)+9*10^113887-7)/9 is 3-PRP! (2553.5794s+0.0694s)