4103163 · 245007 - 183009063 · 225003 - 1
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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:4103163 · 245007 - 183009063 · 225003 - 1
Verification status (*):Proven
Official Comment:Arithmetic progression (4,d=1367721*2^45007-183009063*2^25002)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p199 : Broadhurst, NewPGen, OpenPFGW
Decimal Digits:13556   (log10 is 13555.070133619)
Rank (*):70145 (digit rank is 9)
Entrance Rank (*):42415
Currently on list? (*):short
Submitted:6/3/2010 08:55:52 CDT
Last modified:6/3/2010 09:20:24 CDT
Database id:92976
Status Flags:none
Score (*):33.3824 (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.
Arithmetic Progressions of Primes (archivable class *)
Prime on list: yes, rank 5, weight 44.1018149870799
Subcategory: "Arithmetic progression (4,d=*)"
(archival tag id 210699, tag last modified 2016-03-15 13:57:14)

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -o -f -q"4103163*2^45007-183009063*2^25003-1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 3990694
4103163*2^45007-183009063*2^25003-1 has no small factor.
[Elapsed time: 4.579 seconds]
modified2011-12-27 16:48:39
created2010-06-03 09:05:23

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tp -q"4103163*2^45007-183009063*2^25003-1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 4103163*2^45007-183009063*2^25003-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 11, base 1+sqrt(11)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(6144,21) to FFT(6144,20)
Reduced from FFT(6144,20) to FFT(6144,19)
Reduced from FFT(6144,19) to FFT(6144,18)
Reduced from FFT(6144,18) to FFT(6144,17)
Reduced from FFT(6144,17) to FFT(6144,16)
90074 bit request FFT size=(6144,16)
Calling Brillhart-Lehmer-Selfridge with factored part 55.53%
4103163*2^45007-183009063*2^25003-1 is prime! (71.7400s+0.0000s)
[Elapsed time: 72.00 seconds]
modified2010-10-13 12:41:37
created2010-06-03 09:09:19

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.