1372930131072 + 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:1372930131072 + 1
Verification status (*):Proven
Official Comment:Generalized Fermat
Proof-code(s): (*):g236 : Heuer, GFN17Sieve, GFNSearch, Proth.exe
Decimal Digits:804474   (log10 is 804473.850420117)
Rank (*):853 (digit rank is 1)
Entrance Rank (*):5
Currently on list? (*):short
Submitted:9/22/2003 03:35:09 CDT
Last modified:9/22/2003 03:35:09 CDT
Database id:66324
Status Flags:none
Score (*):45.9653 (normalized score 6.8788)

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 215
Subcategory: "Generalized Fermat"
(archival tag id 204695, tag last modified 2019-09-11 09:50:25)

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.
machineLinux P4 2.8GHz
notesCommand: /home/caldwell/client/pfgw -f -t -q"1372930^131072+1" 2>&1
PFGW Version 20030811.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 313234612
Running N-1 test using base 3
Primality testing 1372930^131072+1 [N-1, Brillhart-Lehmer-Selfridge]
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(393216,19) to FFT(393216,18)
Reduced from FFT(393216,18) to FFT(393216,17)
Reduced from FFT(393216,17) to FFT(393216,16)
5344818 bit request FFT size=(393216,16)
Calling Brillhart-Lehmer-Selfridge with factored part 36.71%
1372930^131072+1 is prime! (-933.3621s+0.2200s)
modified2003-09-27 02:23:03
created2003-09-22 03:53:01

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.