
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:  17684828^{65536} + 1 
Verification status (*):  Proven 
Official Comment:  Generalized Fermat 
Proofcode(s): (*):  g410 : Anonymous, AthGFNSieve, GFNSearch, GFN16Sieve, Proth.exe 
Decimal Digits:  474979 (log_{10} is 474978.76866911) 
Rank (*):  3322 (digit rank is 1) 
Entrance Rank (*):  60 
Currently on list? (*):  yes 
Submitted:  8/4/2007 01:01:44 CDT 
Last modified:  8/4/2007 11:33:00 CDT 
Database id:  81870 
Status Flags:  none 
Score (*):  44.3474 (normalized score 1.3427) 

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 752
Subcategory: "Generalized Fermat"
(archival tag id 204703, tag last modified 20191021 08:50:20)
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  81870 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  Command: /home/caldwell/client/TrialDiv/TrialDiv q 1 17684828 65536 1 2>&1 [Elapsed time: 8.032 seconds]

modified  20070912 06:50:18 
created  20070804 01:22:01 
id  92852 

field  value 
prime_id  81870 
person_id  9 
machine  RedHat P4 P4 
what  prime 
notes  Command: /home/caldwell/client/pfgw t q"17684828^65536+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 17684828^65536+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(196608,19) to FFT(196608,18) Reduced from FFT(196608,18) to FFT(196608,17) 3155700 bit request FFT size=(196608,17) Calling BrillhartLehmerSelfridge with factored part 39.26% 17684828^65536+1 is prime! (36598.6101s+0.1159s) [Elapsed time: 36599 seconds]

modified  20070912 06:50:18 
created  20070804 01:23:01 
id  92856 

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
