659 · 2617815 + 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.

Description:659 · 2617815 + 1
Verification status (*):Proven
Official Comment (*):Divides Fermat F(617813)
Proof-code(s): (*):L732 : Embling, Srsieve, PrimeGrid, LLR
Decimal Digits:185984   (log10 is 185983.66565656)
Rank (*):31145 (digit rank is 1)
Entrance Rank (*):1194
Currently on list? (*):short
Submitted:4/1/2009 19:03:50 CDT
Last modified:4/1/2009 19:50:37 CDT
Database id:87401
Status Flags:none
Score (*):41.4647 (normalized score 0.0514)

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.
Fermat Divisors (archivable *)
Prime on list: yes, rank 19, weight 47.955505366934
Subcategory: "Divides Fermat"
(archival tag id 208960, tag last modified 2021-01-16 15:20:20)

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.
fieldvalue
prime_id87401
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 659 2 617815 1 2>&1 [Elapsed time: 12.656 seconds]
modified2020-07-07 17:30:38
created2009-04-01 19:05:02
id104166

fieldvalue
prime_id87401
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"659*2^617815+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 659*2^617815+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(81920,20) to FFT(81920,19) Reduced from FFT(81920,19) to FFT(81920,18) Reduced from FFT(81920,18) to FFT(81920,17) Reduced from FFT(81920,17) to FFT(81920,16) 1235658 bit request FFT size=(81920,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 659*2^617815+1 is prime! (-2085.8273s+0.0000s) [Elapsed time: 38.10 minutes]
modified2020-07-07 17:30:38
created2009-04-01 19:08:01
id104167

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.