7*(10^3-1)/9 - 2*10^1
*** VFYPR 1.13F  F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 
N=(75*10^3-57)/99
N=757
*** N is prime!
Time: 0 sec


7*(10^15-1)/9 - 2*10^7
== ID:B2813040BF294 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 777777757777777

Decimal size = 15
Binary size = 50

Started 11/01/2002 06:51:31 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.


7*(10^27-1)/9 - 2*10^13
== ID:B2813040A92B4 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 777777777777757777777777777

Decimal size = 27
Binary size = 90

Started 11/01/2002 06:50:01 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.


7*(10^117-1)/9 - 2*10^58
== ID:B28130408DE1A =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 777777777777777777777777777777777777777777777777777777777757\
    777777777777777777777777777777777777777777777777777777777

Decimal size = 117
Binary size = 389

Started 11/01/2002 06:48:10 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.


7*(10^259-1)/9 - 2*10^129
== ID:B2813040673FA =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777577777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    7777777777777777777

Decimal size = 259
Binary size = 861

Started 11/01/2002 06:45:31 PM
Running time 39s

Candidate certified prime

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

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


7*(10^507-1)/9 - 2*10^253
== ID:B280A00AEDC74 =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777757777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777777777777777777777777777777777777\
    777777777777777777777777777

Decimal size = 507
Binary size = 1684

Started 10/23/2002 03:10:59 AM
Running time 4mn 36s

Candidate certified prime

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

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

7*(10^3315-1)/9 - 2*10^1657

Darren Bedwell used Primo to prove this PWP prime.

The certificates are posted to his weblog :

Blog: Zero Sink 
Post: Primo certificate for 
(7*(10^3315-1)/9)-2*10^1657 
Link: http://zerosink.blogspot.com/2010/09/primo-certificate-for-7103315-19.html

[PRIMO - Primality Certificate]
Version=3.0.9
WebSite=http://www.ellipsa.eu/
Format=3
ID=B3350033263DB
Created=09/17/2010 02:54:11 PM
TestCount=468
Status=Candidate certified prime

[Comments]
Write any comment here

[Running Times]
Initialization=15.57s
1stPhase=54h 34mn 50s
2ndPhase=15h 31mn 21s
Total=70h 6mn 27s

[Candidate]
File=C:\Documents and Settings\dbedwell\Desktop\primes\primo\work\nearrep797.in
Expression=(7*(10^3315-1)/9)-2*10^1657
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
HexadecimalSize=2753 DecimalSize=3315 BinarySize=11012

7*(10^4489-1)/9 - 2*10^2244

Darren Bedwell used Primo to prove this PWP prime.

The certificates are posted to his weblog :

Blog: Zero Sink 
Post: 7*(10^4489-1)/9-2*10^2244 is prime. 
Link: http://zerosink.blogspot.com/2010/11/7104489-19-2102244-is-prime.html

[PRIMO - Primality Certificate]
Version=3.0.9
WebSite=http://www.ellipsa.eu/
Format=3
ID=B337702A08104
Created=10/26/2010 12:15:08 PM
TestCount=610
Status=Candidate certified prime

[Comments]
Write any comment here

[Running Times]
Initialization=32.90s
1stPhase=215h 50mn 58s
2ndPhase=66h 2mn 42s
Total=281h 54mn 14s

[Candidate]
File=C:\Documents and Settings\dbedwell\Desktop\primes\primo\work\prp2244.in
Expression=7*(10^4489-1)/9-2*10^2244
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
HexadecimalSize=3728 DecimalSize=4489 BinarySize=14912


7*(10^4875-1)/9 - 2*10^2437
Xinyao Chen informs me (May 19, 2022) that this number is
now a proven palindromic wing prime.
Proof was done by Masaki UKAI on January 23, 2020.

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


7*(10^15849-1)/9 - 2*10^7924
C:\pfgw>pfgw64 -q"7*(10^15849-1)/9-2*10^7924"
PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6]

7*(10^15849-1)/9-2*10^7924 is 3-PRP! (1.8878s+0.0005s)


7*(10^19807-1)/9 - 2*10^9903
C:\pfgw>pfgw64 -q"7*(10^19807-1)/9-2*10^9903"
PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6]

7*(10^19807-1)/9-2*10^9903 is 3-PRP! (3.4874s+0.0005s)


7*(10^23799-1)/9 - 2*10^11899
C:\pfgw>pfgw64 -q"7*(10^23799-1)/9-2*10^11899"
PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6]

7*(10^23799-1)/9-2*10^11899 is 3-PRP! (5.2659s+0.0004s)


7*(10^36315-1)/9 - 2*10^18157
C:\pfgw>pfgw64 -q"7*(10^36315-1)/9-2*10^18157"
PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6]

7*(10^36315-1)/9-2*10^18157 is 3-PRP! (12.1503s+0.0006s)


7*(10^37915-1)/9 - 2*10^18957
C:\pfgw>pfgw64 -q"7*(10^37915-1)/9-2*10^18957"
PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6]

7*(10^37915-1)/9-2*10^18957 is 3-PRP! (13.7118s+0.0006s)


7*(10^47331-1)/9 - 2*10^23665
C:\pfgw>pfgw64 -q"7*(10^47331-1)/9-2*10^23665"
PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6]

7*(10^47331-1)/9-2*10^23665 is 3-PRP! (22.0199s+0.0007s)


7*(10^211219-1)/9 - 2*10^105609
Primality testing (7*10^(2*105609+1)-18*10^105609-7)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge]         
Running N-1 test using base 3
Running N+1 test using discriminant 19, base 3+sqrt(19)
Calling N-1 BLS with factored part 0.00% and helper 0.00% (0.01% proof)

(7*10^(2*105609+1)-18*10^105609-7)/9 is Fermat and Lucas PRP! (6983.3030s+0.0308s) 









 

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( © All rights reserved ) - Last modified : October 12, 2023.

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