35 · 2831411 + 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

This prime's information:

Description:35 · 2831411 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(831410,3)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):g279 : Cooper, NewPGen, PRP, Proth.exe
Decimal Digits:250282   (log10 is 250281.19379303)
Rank (*):22913 (digit rank is 1)
Entrance Rank (*):160
Currently on list? (*):no
Submitted:6/5/2006 23:44:34 CDT
Last modified:7/7/2006 00:52:55 CDT
Database id:77910
Status Flags:none
Score (*):42.3781 (normalized score 0.1047)

Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper.  Such primes are tracked with archival tags.
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 28, weight 45.933548120058
Subcategory: "Divides GF(*,3)"
(archival tag id 187116, tag last modified 2021-02-26 11:20:20)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Curtis Cooper writes (11 Sep 2014):  (report abuse)
35*2^831411+1 is a Factor of GF(831410,3)

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.
machineWinXP Pent_M 1.7GHz Laptop
notesCommand: pfgw.exe -n -t -q"35*2^831411+1" 2>&1 PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Running N-1 test using base 3 N-1: 35*2^831411+1 622Primality testing 35*2^831411+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 35*2^831411+1 is prime! (9137.9324s+0.0457s) 500/831418 [Elapsed time: 9138 seconds]
modified2020-07-07 17:30:42
created2006-06-06 00:44:43

machineGenToo P3 400MHz
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 35 2 831411 1 2>&1 [Elapsed time: 9.839 seconds]
modified2020-07-07 17:30:42
created2006-07-07 00:52:45

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.