513 · 2683547 - 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:513 · 2683547 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L701 : Davies, Srsieve, NPLB, LLR
Decimal Digits:205771   (log10 is 205770.86056349)
Rank (*):30666 (digit rank is 1)
Entrance Rank (*):835
Currently on list? (*):no
Submitted:5/15/2009 09:27:44 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):12/17/2011 01:33:14 UTC
Database id:88290
Status Flags:none
Score (*):41.7758 (normalized score 0.0411)

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_id88290
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 513 2 683547 -1 2>&1 [Elapsed time: 10.095 seconds]
modified2020-07-07 22:30:38
created2009-05-15 09:35:01
id105942

fieldvalue
prime_id88290
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/llr.pl 513*2^683547-1 2>&1 Starting Lucas Lehmer Riesel prime test of 513*2^683547-1 Using Irrational Base DWT : Mersenne fftlen = 40960, Used fftlen = 49152 V1 = 3 ; Computing U0... V1 = 3 ; Computing U0...done. Starting Lucas-Lehmer loop... 513*2^683547-1 is prime! Time : 925.983 sec. [Elapsed time: 15.43 minutes]
modified2020-07-07 22:30:38
created2009-05-15 09:38:01
id105943

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