58185 · 658185 - 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:58185 · 658185 - 1
Verification status (*):Proven
Official Comment (*):Generalized Woodall
Proof-code(s): (*):p77 : Harvey, MultiSieve, GenWoodall, OpenPFGW
Decimal Digits:45282   (log10 is 45281.495314611)
Rank (*):62527 (digit rank is 1)
Entrance Rank (*):3684
Currently on list? (*):no
Submitted:12/17/2003 17:51:49 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:67727
Status Flags:none
Score (*):37.1111 (normalized score 0.0003)

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 Woodall (archivable *)
Prime on list: no, rank 133
Subcategory: "Generalized Woodall"
(archival tag id 190492, tag last modified 2024-02-26 15:37:18)

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.
fieldvalue
prime_id67727
person_id9
machineLinux P4 2.8GHz
whatprime
notesCommand: /home/caldwell/client/pfgw -f -tp -q"58185*6^58185-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 58185*6^58185-1 [N+1, Brillhart-Lehmer-Selfridge] trial factoring to 14601339 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(20480,20) to FFT(20480,19) Reduced from FFT(20480,19) to FFT(20480,18) Reduced from FFT(20480,18) to FFT(20480,17) Reduced from FFT(20480,17) to FFT(20480,16) 300860 bit request FFT size=(20480,16) Calling Brillhart-Lehmer-Selfridge with factored part 61.31% 58185*6^58185-1 is prime! (2660.9077s+0.0031s)
modified2020-07-07 22:30:47
created2003-12-17 18:15:16
id72665

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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