5 · 21777515 + 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:5 · 21777515 + 1
Verification status (*):Proven
Official Comment:Divides GF(1777511,5), GF(1777514,6)
Proof-code(s): (*):p148 : Yama, Noda, Nohara, NewPGen, MatGFN, PRP, OpenPFGW
Decimal Digits:535087   (log10 is 535086.031712666)
Rank (*):2421 (digit rank is 1)
Entrance Rank (*):19
Currently on list? (*):short
Submitted:4/14/2005 19:13:10 CDT
Last modified:4/14/2005 19:13:10 CDT
Database id:74133
Status Flags:none
Score (*):44.7134 (normalized score 1.7871)

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 Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 13, weight 46.3228692051154
Subcategory: "Divides GF(*,6)"
(archival tag id 187047, tag last modified 2020-01-28 18:20:18)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 12, weight 46.3228692051154
Subcategory: "Divides GF(*,5)"
(archival tag id 187046, tag last modified 2019-10-16 18:20:19)

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"5*2^1777515+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 5*2^1777515+1 [N-1, Brillhart-Lehmer-Selfridge]
trial factoring to 203270581
Running N-1 test using base 3
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(229376,19) to FFT(229376,18)
Reduced from FFT(229376,18) to FFT(229376,17)
Reduced from FFT(229376,17) to FFT(229376,16)
3555044 bit request FFT size=(229376,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
5*2^1777515+1 is prime! (67418.7106s+0.0014s)
modified2005-04-18 11:33:10
created2005-04-14 19:23:01

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