4153 · 21035292 + 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:4153 · 21035292 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L3173 : Zhou2, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:311658   (log10 is 311657.56463289)
Rank (*):13996 (digit rank is 1)
Entrance Rank (*):2167
Currently on list? (*):no
Submitted:1/16/2013 00:11:59 CDT
Last modified:1/16/2013 01:20:25 CDT
Removed (*):10/7/2013 04:35:14 CDT
Database id:110733
Status Flags:none
Score (*):43.0525 (normalized score 0.3896)

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_id110733
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 4153 2 1035292 1 2>&1
[Elapsed time: 9.610 seconds]
modified2013-02-02 20:51:49
created2013-01-16 00:18:11
id151740

fieldvalue
prime_id110733
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"4153*2^1035292+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 4153*2^1035292+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
4153*2^1035292+1 is prime! (2506.9486s+0.0008s)
[Elapsed time: 41.78 minutes]
modified2013-02-02 20:51:49
created2013-01-16 00:38:01
id151742

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.