
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:  (2^{281621} + 1)^{2}  2 
Verification status (*):  Proven 
Official Comment:  
Proofcode(s): (*):  p89 : Emmanuel, OpenPFGW 
Decimal Digits:  169553 (log_{10} is 169552.736817772) 
Rank (*):  29704 (digit rank is 1) 
Entrance Rank (*):  347 
Currently on list? (*):  no 
Submitted:  10/9/2005 08:15:23 CDT 
Last modified:  10/10/2005 03:19:33 CDT 
Removed (*):  10/26/2010 11:01:27 CDT 
Database id:  75878 
Status Flags:  none 
Score (*):  41.1801 (normalized score 0.0662) 

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  75878 
person_id  9 
machine  Linux P4 2.8GHz 
what  prime 
notes  Command: /home/caldwell/client/pfgw f tc q"(2^281621+1)^22" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (2^281621+1)^22 [N1/N+1, BrillhartLehmerSelfridge] trial factoring to 59879187 Running N1 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)^22 is prime! (946.5011s+0.0200s) [Elapsed time: 61891 seconds]

modified  20051019 12:27:07 
created  20051009 10:08:02 
id  81072 

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
