8*(10^7-1)/9 + (10^6+1)
run"aprt-cle
Test number  N=? 9888889

Preparatory test
    Pass !

 9888889 is prime.
  0:00:00
OK

Proved prime with 'Ubasic - APRT-CLE.UB'
by Patrick De Geest using a Pentium III 650 MHz chip.


8*(10^73-1)/9 + (10^72+1)
== ID:B28690072192E =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 988888888888888888888888888888888888888888888888888888888888\
    8888888888889

Decimal size = 73
Binary size = 243


Started 01/26/2003 02:04:37 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.


8*(10^97-1)/9 + (10^96+1)
== ID:B286900921A4E =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 988888888888888888888888888888888888888888888888888888888888\
    8888888888888888888888888888888888889

Decimal size = 97
Binary size = 323


Started 01/26/2003 02:39:34 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.


8*(10^115-1)/9 + (10^114+1)
== ID:B286903549DCE =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 988888888888888888888888888888888888888888888888888888888888\
    8888888888888888888888888888888888888888888888888888889

Decimal size = 115
Binary size = 383


Started 01/26/2003 03:31:17 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.


8*(10^205-1)/9 + (10^204+1)
== ID:B286905243F4C =============================================

PRIMO 1.2.1 - Primality Certificate

-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 988888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    888888888888888888888888888888888888888888888888888888888888\
    8888888888888888888888889

Decimal size = 205
Binary size = 681


Started 01/26/2003 11:57:41 PM
Running time 10s

Candidate certified prime

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

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


8*(10^985-1)/9 + (10^984+1)
[PRIMO - Primality Certificate]
Version=2.0.0 - beta 3
Format=2
ID=B286F040DEDC4
Created=02/01/2003 06:53:41 PM
TestCount=166
Status=Candidate certified prime

[Candidate]
File=C:\Program Files\Primo200\pdp989_985.in
Expression=8*(10^985-1)/9 + (10^(983+1)+1)

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

HexadecimalSize=819
DecimalSize=985
BinarySize=3273

[Running Times]
Initialization=3.43s
1stPhase=2h 18mn 12s
2ndPhase=16mn 51s
Total=2h 35mn 8s


Proved prime with 'Primo 2.0.0 - beta 3'
by Patrick De Geest using a Pentium III 650 MHz chip.


8*(10^1227-1)/9 + (10^1226+1)
[PRIMO - Primality Certificate]
Version=2.1.1
WebSite=http://www.ellipsa.net/
Format=3
ID=B29050085869E
Created=07/01/2003 02:25:52 AM
TestCount=182
Status=Candidate certified prime

[Running Times]
Initialization=1.89s
1stPhase=2h 15mn 4s
2ndPhase=16mn 10s
Total=2h 31mn 17s

[Candidate]
File=C:\Primo IN & OUT files\PDP1227.in
Expression=8*(10^1227-1)/9+(10^1226+1)

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

HexadecimalSize=1019
DecimalSize=1227
BinarySize=4076


Proved prime with 'Primo 2.1.1'
by Patrick De Geest using a 3000 MHz Pentium 4 cpu.
Certificate Primo-B29050085869E-01.out available by
simple email request (173 KB).

8*(10^4795-1)/9 + (10^4794+1)

Primo certificate by courtesy of Ray Chandler (Feb 7, 2013) from factordb.com

http://factordb.com/cert.php?id=1000000000009854818


[PRIMO - Primality Certificate]
Version=4.0.1 - LX64
WebSite=http://www.ellipsa.eu/
Format=3
ID=B36B8049DC23D
Created=02-05-2013 09:30:58 pm
TestCount=593
Status=Candidate certified prime

[Comments]
Put here any comment...

[Running Times]
Initialization=11.18s
1stPhase=79033s
2ndPhase=16126s
Total=95170s

[Candidate]
File=/home/ray/Documents/primo/fdb_knrr/pdp-4795-98w9/primo_1000000000009854818.in

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

HexadecimalSize=3983
DecimalSize=4795
BinarySize=15929


8*(10^20721-1)/9 + (10^20720+1)
3-PRP!


8*(10^133581-1)/9 + (10^133580+1)
By Serge Batalov dd. May 15, 2010.

UID: Batalov/Q6600F, 89*10^133580+1/9 is a probable prime! Wd1: 1E7E05E5,00000000

Tools : srsieve, sr1sieve, Prime95 and PFGW 3.3.3


8*(10^411591-1)/9 + (10^411590+1)
By Serge Batalov dd. September 21, 2014.

(89*10^411590+1)/9 is base 3-Strong Fermat PRP! (411591 decimal digits)  Time : 971.723 sec.

Tools used: srsieve and LLR; validated in a few bases with PFGW.
 

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( © All rights reserved ) - Last modified : March 16, 2023.
Patrick De Geest - Belgium flag - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com