2 · 31010743 - 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:2 · 31010743 - 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L426 : Jaworski, Srsieve, Rieselprime, LLR
Decimal Digits:482248   (log10 is 482247.26938911)
Rank (*):5469 (digit rank is 1)
Entrance Rank (*):191
Currently on list? (*):no
Submitted:9/1/2011 10:28:03 CDT
Last modified:9/1/2011 16:50:23 CDT
Removed (*):7/10/2021 18:02:03 CDT
Database id:101433
Status Flags:none
Score (*):44.394 (normalized score 0.9382)

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.

David Broadhurst writes (11 Sep 2014):  (report abuse)
See the OEIS sequence A003307 for the distribution of primes of this form.

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 2 3 1010743 -1 2>&1 [Elapsed time: 10.365 seconds]
modified2020-07-07 17:30:31
created2011-09-01 10:35:01

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tp -q"2*3^1010743-1" 2>&1 PFGW Version [GWNUM 26.5] Primality testing 2*3^1010743-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 2*3^1010743-1 is prime! (21242.8007s+0.0351s) [Elapsed time: 5.90 hours]
modified2020-07-07 17:30:31
created2011-09-01 10:38:01

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