253 · 21086068 + 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:253 · 21086068 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L1446 : Harvey, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:326942   (log10 is 326941.44845131)
Rank (*):20833 (digit rank is 1)
Entrance Rank (*):440
Currently on list? (*):no
Submitted:5/20/2011 23:07:39 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):1/15/2014 18:00:49 UTC
Database id:100143
Status Flags:none
Score (*):43.1997 (normalized score 0.1707)

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_id100143
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"253*2^1086068+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 253*2^1086068+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 253*2^1086068+1 is prime! (2521.4134s+0.0009s) [Elapsed time: 42.03 minutes]
modified2020-07-07 22:30:31
created2011-05-20 23:08:01
id129856

fieldvalue
prime_id100143
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 253 2 1086068 1 2>&1 [Elapsed time: 10.148 seconds]
modified2020-07-07 22:30:31
created2011-05-20 23:18:01
id129857

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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