15 · 24800315 + 1
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help)value
Description:15 · 24800315 + 1
Verification status (*):Proven
Official Comment:Divides GF(4800313,3), GF(4800310,5)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L1754 : Hubbard, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:1445040   (log10 is 1445039.979727)
Rank (*):147 (digit rank is 1)
Entrance Rank (*):144
Currently on list? (*):short
Submitted:10/16/2019 15:50:11 CDT
Last modified:10/16/2019 18:20:17 CDT
Database id:130039
Status Flags:TrialDiv
Score (*):47.7622 (normalized score 40.3616)

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 Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 4, weight 50.4703183503329
Subcategory: "Divides GF(*,3)"
(archival tag id 223585, tag last modified 2019-10-16 18:20:22)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 3, weight 50.4703183503329
Subcategory: "Divides GF(*,5)"
(archival tag id 223586, tag last modified 2019-10-16 18:20:22)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

PrimeGrid writes (16 Oct 2019): 
Divides GF(4800313,3), GF(4800310,5)
Divides xGF(4800313,5,3), xGF(4800312,9,5), xGF(4800314,11,4), xGF(4800314,12,11)

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_id130039
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"15*2^4800315+1" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 15*2^4800315+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


15*2^4800315+1 is prime! (7958.0766s+0.0017s)
[Elapsed time: 2.21 hours]
modified2019-10-16 18:03:39
created2019-10-16 15:51:01
id175724

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.