11922002779 · (2172486 - 286243) + 286245 - 5

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:11922002779 · (2172486 - 286243) + 286245 - 5
Verification status (*):PRP
Official Comment (*):Consecutive primes arithmetic progression (1,d=6)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p408 : Batalov, PolySieve, OpenPFGW
Decimal Digits:51934   (log10 is 51933.536181316)
Rank (*):56849 (digit rank is 4)
Entrance Rank (*):56531
Currently on list? (*):no
Submitted:5/3/2022 18:51:31 CDT
Last modified:5/3/2022 19:37:19 CDT
Database id:133896
Status Flags:Verify, TrialDiv
Score (*):37.5341 (normalized score 0.0008)

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.

User comments about this prime (disclaimer):

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Serge Batalov writes (3 May 2022):  (report abuse)
The N+1 proof helper is 2^86243-1.

Also called Sexy primes

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_id133896
person_id9
machineUsing: Dual Intel Xeon Gold 5222 CPUs 3.8GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"11922002779*(2^172486-2^86243)+2^86245-5" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 11922002779*(2^172486-2^86243)+2^86245-5 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 7 Running N+1 test using discriminant 17, base 1+sqrt(17) Calling N+1 BLS with factored part 0.02% and helper 0.02% (0.09% proof) 11922002779*(2^172486-2^86243)+2^86245-5 is Fermat and Lucas PRP! (91.8216s+0.0001s) [Elapsed time: 1.53 minutes]
modified2022-07-11 13:21:44
created2022-05-03 18:56:01
id179618

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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