(V(49596, 1, 3375) + 1)/(V(49596, 1, 675) + 1)
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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.
Proof-code(s): (*):x25 : Water, Broadhurst, Primo, OpenPFGW
Decimal Digits:12678   (log10 is 12677.7059581125)
Rank (*):64254 (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 2013-04-02 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.

David Broadhurst writes (5 Jan 2006): 
KP proof with helpers in http://physics.open.ac.uk/~dbroadhu/cert/b10125n.zip

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.
fieldvalue
prime_id76675
person_id9
machineLinux P4 2.8GHz
whattrial_divided
notesPFGW 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]
modified2006-01-18 12:45:08
created2006-01-05 14:52:01
id82318

fieldvalue
prime_id76675
person_id9
machineLinux P4 2.8GHz
whatprp
notesCommand: /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) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 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 N-1 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 N-1 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]
modified2006-01-18 12:45:08
created2006-01-05 17:32:21
id82320

Query times: 0.0004 seconds to select prime, 0.0001 seconds to seek comments.