35 · 2768063 + 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:35 · 2768063 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(768062,3)
Proof-code(s): (*):L126 : Keiser, NewPGen, LLR
Decimal Digits:231212   (log10 is 231211.54562771)
Rank (*):24622 (digit rank is 1)
Entrance Rank (*):161
Currently on list? (*):no
Submitted:12/30/2005 16:58:59 CDT
Last modified:12/30/2005 20:20:53 CDT
Database id:76606
Status Flags:none
Score (*):42.1344 (normalized score 0.0821)

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: no, rank 31, weight 45.689799435851
Subcategory: "Divides GF(*,3)"
(archival tag id 187127, tag last modified 2021-02-26 11:20:20)

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.
machineLinux P4 2.8GHz
notesCommand: /home/caldwell/client/pfgw -f -t -q"35*2^768063+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 35*2^768063+1 [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 83322188 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(98304,20) to FFT(98304,19) Reduced from FFT(98304,19) to FFT(98304,18) Reduced from FFT(98304,18) to FFT(98304,17) Reduced from FFT(98304,17) to FFT(98304,16) 1536146 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 35*2^768063+1 is prime! (11156.7806s+0.0007s) [Elapsed time: 11156 seconds]
modified2020-07-07 17:30:43
created2005-12-30 17:14:57

machineLinux P4 2.8GHz
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 35 2 768063 1 2>&1 [Elapsed time: 16.503 seconds]
modified2020-07-07 17:30:43
created2005-12-30 17:22:01

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.