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: (2281621+1)2-2 Verification status (*): Proven Official Comment: Proof-code(s): (*): p89 : Emmanuel, OpenPFGW Decimal Digits: 169553   (log10 is 169552.736817772) Rank (*): 3009 (digit rank is 1) Entrance Rank (*): 347 Currently on list? (*): yes Submitted: 10/9/2005 08:15:23 CDT Last modified: 10/10/2005 03:19:33 CDT Database id: 75878 Status Flags: none Score (*): 41.1801 (normalized score 1.6032)

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 75878 person_id 9 machine Linux P4 2.8GHz what prime notes Command: /home/caldwell/client/pfgw -f -tc -q"(2^281621+1)^2-2" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (2^281621+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 59879187 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) 1126494 bit request FFT size=(65536,18) Running N+1 test using discriminant 7, base 6+sqrt(7) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) 1126502 bit request FFT size=(65536,18) Running N+1 test using discriminant 7, base 9+sqrt(7) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) 1126502 bit request FFT size=(65536,18) Calling N+1 BLS with factored part 50.01% and helper 0.00% (150.02% proof) (2^281621+1)^2-2 is prime! (-946.5011s+0.0200s) [Elapsed time: 61891 seconds] modified 2005-10-19 12:27:07 created 2005-10-09 10:08:02 id 81072