145310262144 + 1
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help
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:145310262144 + 1
Verification status (*):Proven
Official Comment:Generalized Fermat
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p314 : Hubbard, GenefX64, AthGFNSieve, PrimeGrid, OpenPFGW
Decimal Digits:1353265   (log10 is 1353264.79227886)
Rank (*):164 (digit rank is 1)
Entrance Rank (*):23
Currently on list? (*):short
Submitted:2/9/2011 23:47:24 CDT
Last modified:3/30/2011 22:03:53 CDT
Database id:98160
Status Flags:none
Score (*):47.561 (normalized score 33.4081)

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 (archivable *)
Prime on list: no, rank 41
Subcategory: "Generalized Fermat"
(archival tag id 213124, tag last modified 2019-09-23 11:20:13)

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 (11 Sep 2014): 
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.
machineXeon 4c+4c 3.5GHz
notesCommand: ./pfgw64 -t -q"145310^262144+1" 2>&1
PFGW Version [GWNUM 27.11]
Primality testing 145310^262144+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 60.46%

145310^262144+1 is prime! (46438.4777s+0.0465s)
[Elapsed time: 12.90 hours]
modified2014-12-15 15:47:32
created2014-08-20 21:18:27

machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1 145310 262144 1 2>&1
[Elapsed time: 8.635 seconds]
modified2011-12-27 16:48:34
created2011-02-09 23:48:01

Query times: 0.0005 seconds to select prime, 0.0008 seconds to seek comments.