*** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(13*10^3-31)/99 N=131 *** N is prime! Time: 0 sec
run"aprt-cle
Test number N=? 13331
Preparatory test
Pass !
13331 is prime.
0:00:00
OK
Proved prime with 'Ubasic - APRT-CLE.UB'
by Patrick De Geest using a Pentium III 650 MHz chip.
run"aprt-cle
Test number N=? 1333331
Preparatory test
Pass !
1333331 is prime.
0:00:00
OK
Proved prime with 'Ubasic - APRT-CLE.UB'
by Patrick De Geest using a Pentium III 650 MHz chip.
== ID:B2869008C6612 =============================================
PRIMO 1.2.1 - Primality Certificate
-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 133333333333333333333333333333333333333333333333333333333333\
33333333333333333333333333333333331
Decimal size = 95
Binary size = 313
Started 01/26/2003 02:33:21 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.
== ID:B286903FE413A =============================================
PRIMO 1.2.1 - Primality Certificate
-----------------------------------------------------------------
Candidate
-----------------------------------------------------------------
N = 133333333333333333333333333333333333333333333333333333333333\
333333333333333333333333333333333333333333333333333333333333\
33333333333333333333333333333333333333331
Decimal size = 161
Binary size = 532
Started 01/26/2003 06:36:34 PM
Running time 4s
Candidate certified prime
=================================================================
Proved prime with 'Primo 1.2.1'
by Patrick De Geest using a Pentium III 650 MHz chip.
[PRIMO - Primality Certificate] Version=2.0.0 - beta 3 Format=2 ID=B286A0111B6BE Created=01/27/2003 04:58:58 AM TestCount=51 Status=Candidate certified prime [Candidate] File=C:\Program Files\Primo200\pdp131_361.in Expression=(10^361-1)/3 - 2*(10^(359+1)+1)
| N$=13D2DB934CBE6035AE5C48C0F4425C9378487DF0ADF21A1279E9770C93E488C4093C30F6099EB337D43A5E63CA7F2BECA744B7C2FA2E4AC48DD57ED1902C1AB9F24D03D987732C967224C5880650388526832CEE27D8DA2992FFCEC3444FC007D7ABC2AC0D788A4081555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553 |
C:\Pdp>pfgw -hhd1470.fac -l -tp -q"4*(10^1470-1)/3-1" PFGW Version 1.1 for Windows Output logging to file pfgw.out Primality testing 4*(10^1470-1)/3-1 [N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file hd1470.fac Running N+1 test using discriminant 17, base 1+sqrt(17) Calling Brillhart-Lehmer-Selfridge with factored part 34.47% 4*(10^1470-1)/3-1 is prime! (8.010000 seconds) Helper file and original proof by David Broadhurst. Timing : reproduced on a Pentium III 650 MHz chip.
C:\Pdp>pfgw -hhd2898.fac -l -tp -q"4*(10^2898-1)/3-1" PFGW Version 1.1 for Windows Output logging to file pfgw.out Primality testing 4*(10^2898-1)/3-1 [N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file hd2898.fac Running N+1 test using discriminant 17, base 1+sqrt(17) Calling Brillhart-Lehmer-Selfridge with factored part 33.46% 4*(10^2898-1)/3-1 is prime! (35.920000 seconds) Helper file and original proof by David Broadhurst. Timing : reproduced on a Pentium III 650 MHz chip. Announced via http://groups.yahoo.com/group/primenumbers/message/11084
[PRIMO - Primality Certificate] Version=2.1.1 WebSite=http://www.ellipsa.net/ Format=3 ID=B292502F7CCCA Created=08/02/2003 01:50:15 PM TestCount=447 Status=Candidate certified prime [Running Times] Initialization=21.05s 1stPhase=262h 0mn 59s 2ndPhase=14h 1mn 58s Total=276h 3mn 19s [Candidate] File=C:\Primo IN & OUT files\PDP3095.in Expression=(10^3095-1)/3-2*(10^3094+1)
|
[PRIMO - Primality Certificate] Version=2.2.0 beta 1 WebSite=http://www.ellipsa.net/ Format=3 ID=B29370332744A Created=08/20/2003 02:54:33 PM TestCount=437 Status=Candidate certified prime [Running Times] Initialization=34.86s 1stPhase=153h 56mn 51s 2ndPhase=36h 26mn 30s Total=190h 23mn 56s [Candidate] File=C:\Primo IN & OUT files\PDP3113.in Expression=(10^3113-1)/3-2*(10^3112+1)
|
3-PRP!
3-PRP!
3-PRP!
By Ray Chandler dd. April 15, 2011. PFGW Version 3.4.6.64BIT.20110307.Win_Dev [GWNUM 26.5] Primality testing (4*10^111032-7)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 31, base 2+sqrt(31) Calling N+1 BLS with factored part 0.02% and helper 0.00% (0.06% proof) (4*10^111032-7)/3 is Fermat and Lucas PRP! (5052.1160s+7.9273s)
By Serge Batalov dd. January 15, 2023. Source PRP : https://stdkmd.net/nrr/1/13331.htm#prime
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Patrick De Geest - Belgium
- Short Bio - Some PicturesE-mail address : pdg@worldofnumbers.com