13 · 25523860 + 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:13 · 25523860 + 1
Verification status (*):Proven
Official Comment (*):Divides Fermat F(5523858)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L1204 : Brown1, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:1662849   (log10 is 1662848.66579179)
Rank (*):151 (digit rank is 1)
Entrance Rank (*):115
Currently on list? (*):short
Submitted:1/22/2020 18:56:45 CDT
Last modified:1/22/2020 21:50:20 CDT
Database id:130274
Status Flags:TrialDiv
Score (*):48.1927 (normalized score 54.2608)

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 1, weight 50.7577083594875
Subcategory: "Divides Fermat"
(archival tag id 223680, tag last modified 2020-01-22 21:50:25)

User comments about this prime (disclaimer):

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PrimeGrid writes (24 Jan 2020):  (report abuse)
Divides GF(5523856,11), xGF(5523857,9,5), xGF(5523858,10,9), xGF(5523858,11,2), xGF(5523857,11,4), xGF(5523858,11,8)

For more information, please see the Official Announcement.

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_id130274
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"13*2^5523860+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 13*2^5523860+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 13*2^5523860+1 is prime! (10007.4092s+0.0025s) [Elapsed time: 2.78 hours]
modified2020-07-07 17:30:10
created2020-01-22 19:01:02
id175960

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
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