10223 · 231172165 + 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:10223 · 231172165 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):SB12 : Szabolcs, Srsieve, SoBSieve, ProthSieve, Ksieve, PrimeGrid, LLR, SB
Decimal Digits:9383761   (log10 is 9383760.7043653)
Rank (*):11 (digit rank is 1)
Entrance Rank (*):7
Currently on list? (*):short
Submitted:11/6/2016 18:15:13 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:122473
Status Flags:none
Score (*):53.4922 (normalized score 5287.824)

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 (9 Nov 2016):  (report abuse)
This is the twelfth prime found by the combined Seventeen or Bust / PrimeGrid effort. Five more to go to prove that k=78557 (Selfridge, 1962) is the least odd integer such that all of the numbers k*2^n+1 are composite for integers n > 0 (that is, to show that 78557 is the least Sierpinski number). As of the time of its finding, this is the largest non-Mersenne prime known and the only non-Mersenne prime over four million digits. It is the largest prime ever found at PrimeGrid.

For more details, 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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"10223*2^31172165+1" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 10223*2^31172165+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 10223*2^31172165+1 is prime! (691348.6374s+0.0067s) [Elapsed time: 8.00 days]
modified2020-07-07 22:30:16
created2016-11-06 18:21:01

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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