2575 · 2675314 + 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:2575 · 2675314 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L1204 : Brown1, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:203294   (log10 is 203293.18126906)
Rank (*):23225 (digit rank is 1)
Entrance Rank (*):3516
Currently on list? (*):no
Submitted:8/19/2011 20:27:58 CDT
Last modified:8/19/2011 21:20:24 CDT
Removed (*):11/30/2011 18:52:01 CDT
Database id:101131
Status Flags:none
Score (*):41.7385 (normalized score 0.1045)

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_id101131
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 2575 2 675314 1 2>&1
[Elapsed time: 9.564 seconds]
modified2011-12-27 16:48:30
created2011-08-19 20:35:02
id131822

fieldvalue
prime_id101131
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"2575*2^675314+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 2575*2^675314+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
2575*2^675314+1 is prime! (991.8345s+0.0006s)
[Elapsed time: 16.53 minutes]
modified2011-12-27 16:48:30
created2011-08-19 20:38:01
id131829

Query times: 0.0005 seconds to select prime, 0.0005 seconds to seek comments.