5051 · 21017423 + 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 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:5051 · 21017423 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L1823 : Larsson, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:306279   (log10 is 306278.5446558)
Rank (*):13461 (digit rank is 1)
Entrance Rank (*):1846
Currently on list? (*):no
Submitted:10/7/2012 11:07:26 CDT
Last modified:10/7/2012 12:20:27 CDT
Removed (*):9/13/2013 05:39:23 CDT
Database id:109695
Status Flags:none
Score (*):42.999 (normalized score 0.4194)

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_id109695
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 5051 2 1017423 1 2>&1
[Elapsed time: 9.779 seconds]
modified2012-11-04 23:29:01
created2012-10-07 11:18:01
id149035

fieldvalue
prime_id109695
person_id9
machineRedHat Virtual STEM Server
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"5051*2^1017423+1" 2>&1
PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14]
Primality testing 5051*2^1017423+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
5051*2^1017423+1 is prime! (2035.7851s+0.0634s)
[Elapsed time: 33.93 minutes]
modified2012-11-04 23:29:01
created2012-10-07 11:41:53
id149038

Query times: 0.0004 seconds to select prime, 0.0011 seconds to seek comments.