13 · 21861732 + 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:

Description:13 · 21861732 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(1861731,6)
Proof-code(s): (*):g267 : Grobstich, NewPGen, PRP, Proth.exe
Decimal Digits:560439   (log10 is 560438.28983085)
Rank (*):4347 (digit rank is 1)
Entrance Rank (*):21
Currently on list? (*):short
Submitted:11/14/2005 07:30:01 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:76172
Status Flags:none
Score (*):44.8556 (normalized score 1.0875)

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 18, weight 47.420550839022
Subcategory: "Divides GF(*,6)"
(archival tag id 187043, tag last modified 2023-03-31 01:37:05)

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"13*2^1861732+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 13*2^1861732+1 [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 213504730 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) 3723480 bit request FFT size=(229376,17) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 13*2^1861732+1 is prime! (-371.3584s+0.0000s) [Elapsed time: 39397 seconds]
modified2020-07-07 22:30:43
created2005-11-15 12:17:30

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