350049825 · 235000 + 7703
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

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:350049825 · 235000 + 7703
Verification status (*):PRP
Official Comment:ECPP, consecutive primes arithmetic progression (3,d=3852)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c4 : Broadhurst, Primo
Decimal Digits:10545   (log10 is 10544.593978104)
Rank (*):74669 (digit rank is 6)
Entrance Rank (*):65749
Currently on list? (*):short
Submitted:1/11/2014 16:17:44 CDT
Last modified:1/11/2014 16:51:14 CDT
Database id:116892
Status Flags:Verify, TrialDiv
Score (*):32.6044 (normalized score 0)

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.
Consecutive Primes in Arithmetic Progression (archivable class *)
Prime on list: yes, rank 4
Subcategory: "Consecutive primes in arithmetic progression (3,d=*)"
(archival tag id 217570, tag last modified 2014-03-19 14:52:09)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 126, weight 38.207390424752
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 217571, tag last modified 2019-07-04 05:50:22)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 164
Subcategory: "ECPP"
(archival tag id 217572, tag last modified 2019-10-03 14:20:22)

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.

David Broadhurst writes (11 Sep 2014): 

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -tc -q"350049825*2^35000+7703" 2>&1
PFGW Version [GWNUM 26.5]
Primality testing 350049825*2^35000+7703 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N+1 BLS with factored part 0.10% and helper 0.08% (0.38% proof)
350049825*2^35000+7703 is Fermat and Lucas PRP! (18.5466s+0.0003s)
[Elapsed time: 19.00 seconds]
modified2014-04-01 17:37:38
created2014-01-11 16:27:51

Query times: 0.0002 seconds to select prime, 0.0001 seconds to seek comments.