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: 2389335 + 297837 + 1 Verification status (*): PRP Official Comment: Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): x32 : Renze, Broadhurst, OpenPFGW Decimal Digits: 117202   (log10 is 117201.513361836) Rank (*): 27202 (digit rank is 1) Entrance Rank (*): 976 Currently on list? (*): no Submitted: 3/5/2006 19:19:59 CDT Last modified: 3/5/2006 20:53:02 CDT Removed (*): 4/28/2009 15:26:39 CDT Database id: 77228 Status Flags: Verify Score (*): 40.0432 (normalized score 0.0626)

User comments about this prime (disclaimer):

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David Broadhurst writes (10 Mar 2006): 

This prime has been subjected to deep scrutiny, which will, we hope, continue. Please see the comments attached to the proving code, x32, and in the GP source file, T389335.gp, in what we claim to be the proof of http://physics.open.ac.uk/~dbroadhu/cert/T389335.zip

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.

field value prime_id 77228 person_id 9 machine Linux P4 2.8GHz what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"2^389335+2^97837+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 40384465 2^389335+2^97837+1 has no small factor. [Elapsed time: 395.039 seconds] modified 2006-03-10 10:52:00 created 2006-03-05 19:22:01 id 83446

field value prime_id 77228 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -t -q"2^389335+2^97837+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2^389335+2^97837+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 778680 bit request FFT size=(49152,16) Calling Brillhart-Lehmer-Selfridge with factored part 25.16% 2^389335+2^97837+1 is PRP! (-1884.3273s+0.0000s) [Elapsed time: 5401 seconds] modified 2006-03-10 10:52:00 created 2006-03-05 19:23:01 id 83447