
The hardware and software on this system was updated September 4th.
Please let me know of any problem you encounter.
< caldwell@utm.edu>
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:  (V(49596, 1, 3375) + 1)/(V(49596, 1, 675) + 1) 
Verification status (*):  PRP 
Official Comment:  Lehmer primitive part 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  x25 : Water, Broadhurst, Primo, OpenPFGW 
Decimal Digits:  12678 (log_{10} is 12677.7059581125) 
Rank (*):  65012 (digit rank is 1) 
Entrance Rank (*):  27996 
Currently on list? (*):  short 
Submitted:  1/5/2006 14:39:48 CDT 
Last modified:  1/5/2006 17:35:55 CDT 
Database id:  76675 
Status Flags:  Verify 
Score (*):  33.1752 (normalized score 0) 

Archival tags:
There are certain forms classed as
archivable: these prime may (at times)
remain on this list even if they do not make
the Top 5000 proper. Such primes are tracked with archival
tags.
 Lehmer primitive part (archivable *)
 Prime on list: yes, rank 20
Subcategory: "Lehmer primitive part"
(archival tag id 193641, tag last modified 20130402 14:20:46)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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  76675 
person_id  9 
machine  Linux P4 2.8GHz 
what  trial_divided 
notes  PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] 5081104331...4074178940.........0901545702140599 1/1
trial factoring to 3712713 5081104331...9930750001 has no small factor. [Elapsed time: 35.868 seconds]

modified  20060118 12:45:08 
created  20060105 14:52:01 
id  82318 

field  value 
prime_id  76675 
person_id  9 
machine  Linux P4 2.8GHz 
what  prp 
notes  Command: /home/caldwell/client/pfgw tc q"(lucasV(49596,1,3375)+1)/(lucasV(49596,1,675)+1)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (lucasV(49596,1,3375)+1)/(lucasV(49596,1,675)+1) [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 23 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(5120,21) to FFT(5120,20) Reduced from FFT(5120,20) to FFT(5120,19) Reduced from FFT(5120,19) to FFT(5120,18) Reduced from FFT(5120,18) to FFT(5120,17) 84238 bit request FFT size=(5120,17) Running N1 test using base 31 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(5120,21) to FFT(5120,20) Reduced from FFT(5120,20) to FFT(5120,19) Reduced from FFT(5120,19) to FFT(5120,18) Reduced from FFT(5120,18) to FFT(5120,17) 84238 bit request FFT size=(5120,17) Running N+1 test using discriminant 41, base 8+sqrt(41) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(5120,21) to FFT(5120,20) Reduced from FFT(5120,20) to FFT(5120,19) Reduced from FFT(5120,19) to FFT(5120,18) Reduced from FFT(5120,18) to FFT(5120,17) 84246 bit request FFT size=(5120,17) Calling N1 BLS with factored part 2.29% and helper 0.03% (6.90% proof) (lucasV(49596,1,3375)+1)/(lucasV(49596,1,675)+1) is Fermat and Lucas PRP! (213.8786s+0.0486s) [Elapsed time: 214 seconds]

modified  20060118 12:45:08 
created  20060105 17:32:21 
id  82320 

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
