1768482865536 + 1
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help

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:1768482865536 + 1
Verification status (*):Proven
Official Comment:Generalized Fermat
Proof-code(s): (*):g410 : Anonymous, AthGFNSieve, GFNSearch, GFN16Sieve, Proth.exe
Decimal Digits:474979   (log10 is 474978.76866911)
Rank (*):3808 (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 1.1993)

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 1085
Subcategory: "Generalized Fermat"
(archival tag id 204703, tag last modified 2020-03-26 21:50:24)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1 17684828 65536 1 2>&1
[Elapsed time: 8.032 seconds]
modified2007-09-12 06:50:18
created2007-08-04 01:22:01

machineRedHat P4 P4
notesCommand: /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 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 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 Brillhart-Lehmer-Selfridge with factored part 39.26%
17684828^65536+1 is prime! (36598.6101s+0.1159s)
[Elapsed time: 36599 seconds]
modified2007-09-12 06:50:18
created2007-08-04 01:23:01

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