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: 4391 · 2478827+1 Verification status (*): Proven Official Comment: Proof-code(s): (*): L1046 : Scullin, Srsieve, PrimeGrid, LLR Decimal Digits: 144145   (log10 is 144144.93229723) Rank (*): 4535 (digit rank is 1) Entrance Rank (*): 4382 Currently on list? (*): yes Submitted: 11/5/2009 11:09:06 CDT Last modified: 11/5/2009 11:50:19 CDT Database id: 90750 Status Flags: none Score (*): 40.6804 (normalized score 1.0662)

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 90750 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"4391*2^478827+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 4391*2^478827+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(57344,20) to FFT(57344,19) Reduced from FFT(57344,19) to FFT(57344,18) Reduced from FFT(57344,18) to FFT(57344,17) 957688 bit request FFT size=(57344,17) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 4391*2^478827+1 is prime! (1141.8400s+0.0000s) [Elapsed time: 19.12 minutes] modified 2009-11-05 11:42:08 created 2009-11-05 11:23:01 id 110874

field value prime_id 90750 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 4391 2 478827 1 2>&1 [Ellapsed time: 9.531 seconds] modified 2009-11-05 11:18:11 created 2009-11-05 11:18:01 id 110873