(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 
Link: http://zerosink.blogspot.com/2010/09/primo-certificate-for-103111-134101555.html


[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

[Comments]
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
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
HexadecimalSize=2584 DecimalSize=3111 BinarySize=10333


(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)                     









 

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