
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:  2^{859433}  1 
Verification status (*):  Proven 
Official Comment:  Mersenne 33 
Proofcode(s): (*):  SG : Gage, Slowinski 
Decimal Digits:  258716 (log_{10} is 258715.112263482) 
Rank (*):  18033 (digit rank is 1) 
Entrance Rank (*):  1 
Currently on list? (*):  short 
Submitted:  1/10/1994 
Last modified:  1/10/1994 
Database id:  23 
Status Flags:  none 
Score (*):  42.4801 (normalized score 0.2126) 

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.
 Mersenne (archivable *)
 Prime on list: yes, rank 19
Subcategory: "Mersenne"
(archival tag id 187113, tag last modified 20181221 09:15:32)
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.
field  value 
prime_id  23 
person_id  9 
machine  RedHat P4 P4 
what  prime 
notes  Command: /home/caldwell/client/pfgw tp q"2^8594331" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2^8594331 [N+1, BrillhartLehmerSelfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(114688,20) to FFT(114688,19) Reduced from FFT(114688,19) to FFT(114688,18) Reduced from FFT(114688,18) to FFT(114688,17) Reduced from FFT(114688,17) to FFT(114688,16) 1718882 bit request FFT size=(114688,16) Calling BrillhartLehmerSelfridge with factored part 100.00% 2^8594331 is prime! (13568.8914s+0.0007s) [Elapsed time: 3.77 hours]

modified  20080912 14:12:35 
created  20080806 06:27:42 
id  100213 

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.
