
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:  (5^{95310} + 1)^{2} + 5^{95310} 
Verification status (*):  Proven 
Official Comment:  
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  p82 : Oakes, Broadhurst, OpenPFGW 
Decimal Digits:  133238 (log_{10} is 133237.66222653) 
Rank (*):  34501 (digit rank is 1) 
Entrance Rank (*):  840 
Currently on list? (*):  no 
Submitted:  8/19/2006 11:36:02 CDT 
Last modified:  8/19/2006 15:11:27 CDT 
Removed (*):  8/11/2009 16:40:14 CDT 
Database id:  78328 
Status Flags:  none 
Score (*):  40.4381 (normalized score 0.0367) 

User comments about this prime (disclaimer):
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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  78328 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  Command: /home/caldwell/client/pfgw o f q"(5^95310+1)^2+5^95310" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 46307299 (5^95310+1)^2+5^95310 has no small factor. [Elapsed time: 524.109 seconds]

modified  20070303 21:00:43 
created  20060819 11:52:01 
id  85755 

field  value 
prime_id  78328 
person_id  9 
machine  RedHat P4 P4 
what  prime 
notes  Command: /home/caldwell/client/pfgw tc q"(5^95310+1)^2+5^95310" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (5^95310+1)^2+5^95310 [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 2 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) Reduced from FFT(57344,17) to FFT(57344,16) 885220 bit request FFT size=(57344,16) Running N+1 test using discriminant 7, base 2+sqrt(7) 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) Reduced from FFT(57344,17) to FFT(57344,16) 885228 bit request FFT size=(57344,16) Calling N1 BLS with factored part 50.00% and helper 0.06% (150.06% proof) (5^95310+1)^2+5^95310 is prime! (1799.0819s+0.0300s) [Elapsed time: 11904 seconds]

modified  20070303 21:00:43 
created  20060819 11:53:03 
id  85756 

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.
