Primality Proof of phi(13681,26371)

OpenPFGW

Primality testing Phi(13681,26371) [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 29
Calling Brillhart-Lehmer-Selfridge with factored part 30.09%
Phi(13681,26371) is PRP! (849.1824s+0.0029s)

KP

The Konyagin-Pomerance primality proof is in the PARI script KonPom.gp. The output from this script is in KP.txt.

Helper File

Based on factorization of N-1 and N+1:

Phi(13680,26371)/13082397832081
13082397832081
Phi(570,26371)
Phi(240,26371)/(1201*50092645863361*680272022919884135522023681)
1201
50092645863361
680272022919884135522023681
Phi(228,26371)/(8209*8893*5547697*129252061)
8209
8893
5547697
129252061
Phi(190,26371)/104503991
104503991
Phi(144,26371)/(433*145094113*11977430990088618685582702129)
433
145094113
11977430990088618685582702129
3077295293259686183511334476988304490484164044459610910166546401921
972482930809704756984143932268478291587598230056350756110447679236336145601
Phi(114,26371)/229
229
3053431
23196079876103731
180649042429661509877016002924462046752700637924192918722693845596632789685488226381
241
347041
147709681590669521
7393765976912686719357292001
70409637964007860252647077886881
465314469390598807041578322635125899310793101483823628641
137029
9549240401
23881698251980135612908799126836931609
46313865740922362081430715446962524406814969175466846784085516096025307684810327630643322363265020709808301
1801
64679977
222510841419914252222860665622795969
493632362470087277392339852168948038985818747909383818693057
55381
1013712282421
161822627759941
6021585113481674246780654340092489754421
147517
5653603
35630370313653084836788465466509083235129
11864416859484859662836498726883150355161642410107
4104941496675773937311252927384855966086798690973397874837
181
17551
147151
265770361
8461207623601
12171828166146393744605370670978337653479395980432124726428678555814326501

Prime Factor Certification

Signed Primo certificate for Phi(13680,26371)/13082397832081 (15267 digits): ecpp15267.zip

A signed Primo certificate for Phi(570,26371) (637 digits) is included in: 26371_1368.zip.

Tom Wu

Last modified: Thu Feb 16 00:00:00 PDT 2012