At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help) value Description: 427194 · 113427194 + 1 Verification status (*): Proven Official Comment: Generalized Cullen Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): p310 : Hubbard, Gcwsieve, MultiSieve, PrimeGrid, OpenPFGW Decimal Digits: 877069   (log10 is 877068.4232106) Rank (*): 93 (digit rank is 1) Entrance Rank (*): 57 Currently on list? (*): short Submitted: 1/29/2012 12:01:47 CDT Last modified: 1/30/2012 02:50:24 CDT Database id: 104121 Status Flags: none Score (*): 46.2305 (normalized score 30.4276)

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 Cullen (archivable *)

Prime on list: yes, rank 1
Subcategory: "Generalized Cullen"
(archival tag id 213810, tag last modified 2012-01-30 02:50:25)

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.

PrimeGrid writes (29 Jan 2012): 

For more information, please see the Official Announcement.

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.

field value prime_id 104121 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 427194 113 427194 1 2>&1 [Elapsed time: 9.271 seconds] modified 2012-02-19 19:07:47 created 2012-01-29 12:05:02 id 137832

field value prime_id 104121 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"427194*113^427194+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 427194*113^427194+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 427194*113^427194+1 is prime! (51331.9834s+0.0705s) [Elapsed time: 14.26 hours] modified 2012-02-19 19:07:47 created 2012-01-29 12:08:02 id 137833