1681 · 2612372 + 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:1681 · 2612372 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L1320 : Fredriksen, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:184346   (log10 is 184345.56607246)
Rank (*):30011 (digit rank is 1)
Entrance Rank (*):4869
Currently on list? (*):no
Submitted:1/25/2011 09:05:46 CDT
Last modified:1/25/2011 15:50:23 CDT
Removed (*):1/29/2011 19:18:52 CDT
Database id:97694
Status Flags:none
Score (*):41.4375 (normalized score 0.0605)

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 1598
Subcategory: "Generalized Fermat"
(archival tag id 213100, tag last modified 2020-10-24 09:50:10)

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_id97694
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1681 2 612372 1 2>&1 [Elapsed time: 10.627 seconds]
modified2020-07-07 17:30:32
created2011-01-25 09:21:40
id124782

fieldvalue
prime_id97694
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"1681*2^612372+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 1681*2^612372+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) 1224774 bit request FFT size=(81920,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 1681*2^612372+1 is prime! (-1873.0573s+0.0000s) [Elapsed time: 44.38 minutes]
modified2020-07-07 17:30:32
created2011-01-25 14:56:06
id124809

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