(10^3-1)/3 + 4*10^1
*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0
N=(37*10^3-73)/99
N=373
*** N is prime!
Time: 0 sec

(10^7-1)/3 + 4*10^3
== ID:B2814000E4606 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 3337333

Decimal size = 7
Binary size = 22

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

Started 11/02/2002 12:15:35 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.

(10^15-1)/3 + 4*10^7
== ID:B2814000CCEFC =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 333333373333333

Decimal size = 15
Binary size = 49

Started 11/02/2002 12:13:59 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.

(10^23-1)/3 + 4*10^11
== ID:B2814000B9406 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 33333333333733333333333

Decimal size = 23
Binary size = 75

Started 11/02/2002 12:12:38 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.

(10^27-1)/3 + 4*10^13
== ID:B2814000A529E =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 333333333333373333333333333

Decimal size = 27
Binary size = 89

Started 11/02/2002 12:11:16 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.

(10^35-1)/3 + 4*10^17
== ID:B28140008B376 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 33333333333333333733333333333333333

Decimal size = 35
Binary size = 115

Started 11/02/2002 12:09:30 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.

(10^59-1)/3 + 4*10^29
== ID:B281400071070 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 33333333333333333333333333333733333333333333333333333333333

Decimal size = 59
Binary size = 195

Started 11/02/2002 12:07:42 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.

(10^63-1)/3 + 4*10^31
== ID:B281400050A50 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 333333333333333333333333333333373333333333333333333333333333\
333

Decimal size = 63
Binary size = 208

Started 11/02/2002 12:05:30 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.

(10^67-1)/3 + 4*10^33
== ID:B28140003271C =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 333333333333333333333333333333333733333333333333333333333333\
3333333

Decimal size = 67
Binary size = 221

Started 11/02/2002 12:03:26 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.

(10^155-1)/3 + 4*10^77
== ID:B2814000159D2 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 333333333333333333333333333333333333333333333333333333333333\
333333333333333337333333333333333333333333333333333333333333\
33333333333333333333333333333333333

Decimal size = 155
Binary size = 514

Started 11/02/2002 12:01:28 AM
Running time 3s

Candidate certified prime

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

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

(10^1867-1)/3 + 4*10^933
[PRIMO - Primality Certificate]
Version=2.0.0 - beta 3 - (3)933 7 (3)933
Format=2
ID=B27F302916C46
Created=09/30/2002 11:58:04 AM
TestCount=259
Status=Candidate certified prime

[Running Times]
Initialization=6.36s
1stPhase=14h 32mn 6s
2ndPhase=1h 1mn 6s
Total=15h 33mn 19s

Proved prime with 'Primo 2.0.0 - beta 3' by Jeff Heleen
using a 1.33 GHz Athlon chip.
The file "Primo-B27F302916C46-001.out" is 516KB
and is available on demand by simple email request.

(10^3111-1)/3 + 4*10^1555

Darren Bedwell used Primo to prove this PWP prime.

The certificates are posted to my weblog :

Blog: Zero Sink
Post: Primo Certificate for (10^3111-1)/3+4*10^1555

[PRIMO - Primality Certificate]
Version=3.0.9
WebSite=http://www.ellipsa.eu/
Format=3
ID=B3353030A2DD5
Created=09/20/2010 02:10:11 PM
TestCount=446
Status=Candidate certified prime

Write any comment here

[Running Times]
Initialization=13.01s
1stPhase=29h 45mn 35s
2ndPhase=11h 10mn 54s
Total=40h 56mn 43s

[Candidate]
File=C:\Documents and Settings\dbedwell\Desktop\primes\primo\work\pwps.in
Expression=(10^3111-1)/3+4*10^1555

(10^23517-1)/3 + 4*10^11758
C:\pfgw>pfgw64 -q"(10^23517-1)/3 + 4*10^11758"
PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8]

(10^23517-1)/3 + 4*10^11758 is 3-PRP! (2.8370s+0.0012s)

(10^235415-1)/3 + 4*10^117707
pfgw64 -tc -q"(10^(2*117707+1)+12*10^117707-1)/3"
PFGW Version 3.7.7.64BIT.20130722.Win_Dev [GWNUM 27.11]
Primality testing (10^(2*117707+1)+12*10^117707-1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 2
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N+1 BLS with factored part 0.00% and helper 0.00% (0.01% proof)
(10^(2*117707+1)+12*10^117707-1)/3 is Fermat and Lucas PRP! (9782.3159s+0.0118s)