525806!7 + 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:525806!7 + 1
Verification status (*):Proven
Official Comment:Multifactorial
Proof-code(s): (*):p3 : Dohmen, OpenPFGW
Decimal Digits:397102   (log10 is 397101.28067464)
Rank (*):6534 (digit rank is 1)
Entrance Rank (*):679
Currently on list? (*):no
Submitted:8/20/2012 06:57:27 CDT
Last modified:8/20/2012 15:50:24 CDT
Database id:108892
Status Flags:none
Score (*):43.7972 (normalized score 0.7936)

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.
Multifactorial (tolerated *)
Prime on list: no, rank 7
Subcategory: "Multifactorial"
(archival tag id 214460, tag last modified 2019-05-26 21:50:27)

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"525806!7+1" 2>&1
PFGW Version [GWNUM 26.5]
525806!7+1 1/1 mro=0

trial factoring to 148098407
525806!7+1 has no small factor.
[Elapsed time: 4812.010 seconds]
modified2012-09-15 19:04:20
created2012-08-20 07:05:21

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"525806!7+1" 2>&1
PFGW Version [GWNUM 26.5]
Primality testing 525806!7+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 87793
Calling Brillhart-Lehmer-Selfridge with factored part 33.58%
525806!7+1 is prime! (30414.8908s+5.6386s)
[Elapsed time: 8.45 hours]
modified2012-09-15 19:04:20
created2012-08-20 07:23:01

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