1290733709840 · 2677# + 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:1290733709840 · 2677# + 1
Verification status (*):Proven
Official Comment (*):Cunningham chain 2nd kind (16p-15)
Proof-code(s): (*):p295 : Angel, NewPGen, OpenPFGW
Decimal Digits:1141   (log10 is 1140.7087035523)
Rank (*):121677 (digit rank is 11)
Entrance Rank (*):84036
Currently on list? (*):short
Submitted:1/6/2011 03:38:44 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:97267
Status Flags:none
Score (*):25.6838 (normalized score 0)

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.
Cunningham Chains (2nd kind) (archivable class *)
Prime on list: yes, rank 5, weight 46.295295328156
Subcategory: "Cunningham chain 2nd kind (16p-15)"
(archival tag id 213048, tag last modified 2023-03-11 15:53:59)

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 Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -t -q"1290733709840*2677#+1" 2>&1 PFGW Version [GWNUM 25.14] Primality testing 1290733709840*2677#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2689 Calling Brillhart-Lehmer-Selfridge with factored part 33.57% 1290733709840*2677#+1 is prime! (0.1994s+0.0003s) [Elapsed time: 10.00 seconds]
modified2020-07-07 22:30:32
created2011-01-06 03:50:13

machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1290733709840 2677 # 1 2>&1 [Elapsed time: 161.608 seconds]
modified2020-07-07 22:30:32
created2011-01-06 04:00:38

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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