651 · 2655935 + 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:651 · 2655935 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L888 : Moreno_A, Srsieve, PrimeGrid, LLR
Decimal Digits:197459   (log10 is 197458.92378684)
Rank (*):34601 (digit rank is 1)
Entrance Rank (*):1143
Currently on list? (*):no
Submitted:6/22/2009 19:52:32 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):4/8/2011 18:09:15 UTC
Database id:88971
Status Flags:none
Score (*):41.649 (normalized score 0.0362)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Alessandro Moreno writes (11 Sep 2014):  (report abuse)
Divides xGF(655934,11,7)

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_id88971
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"651*2^655935+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 651*2^655935+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(98304,20) to FFT(98304,19) Reduced from FFT(98304,19) to FFT(98304,18) Reduced from FFT(98304,18) to FFT(98304,17) Reduced from FFT(98304,17) to FFT(98304,16) 1311898 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 651*2^655935+1 is prime! (-1441.6773s+0.0100s) [Elapsed time: 48.03 minutes]
modified2020-07-07 22:30:37
created2009-06-22 19:53:01
id107307

fieldvalue
prime_id88971
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 651 2 655935 1 2>&1 [Elapsed time: 9.921 seconds]
modified2020-07-07 22:30:37
created2009-06-22 20:05:01
id107308

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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