1024 · 31877301 + 1

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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:1024 · 31877301 + 1
Verification status (*):External
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p378 : Batalov, Srsieve, CRUS, LLR, OpenPFGW
Decimal Digits:895704   (log10 is 895703.21890644)
Rank (*):3795 (digit rank is 1)
Entrance Rank (*):160
Currently on list? (*):yes
Submitted:12/15/2014 05:05:01 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:118946
Status Flags:Verify
Score (*):46.295 (normalized score 2.358)

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.

Serge Batalov writes (16 Dec 2014):  (report abuse)
Short summary of findings:
1) Currently (as of Dec/15/2014), there is a mixed bag of this number's character results. It is unclear where the software bug precisely is.
2) this number is a 2-, 3-, 5-, 7-, 11-, 13-, 17-, 19-PRP by Prime95 (mprime 27.9, 28.5 were tested)
3) this number is reported prime by N-1 test with non-AVX (two different FFT sizes) PFGW (with pre-AVX version of PFGW or latest PFGW on non-AVX hardware)
4) this number is reported prime by N-1 test with LLR 3.8.13 on non-AVX hardware, using two different FFT sizes: 256K, 288K, and with FermatBase=5, 7, 11, 19
but
5) this number is reported composite by AVX-enabled versions of PFGW and LLR (however, it is a 3- and 17-SPRP in AVX-FFT LLR)

Verification data:

Some of the very largest primes are externally verified by trusted groups or individuals and we do not reverify them at this site. This is one of those.
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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