
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^{14561}  1)/8074991336582835391 
Verification status (*):  PRP 
Official Comment:  Mersenne cofactor, ECPP 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  c8 : Water, Broadhurst, Primo 
Decimal Digits:  4365 (log_{10} is 4364.3906248) 
Rank (*):  83916 (digit rank is 1) 
Entrance Rank (*):  35224 
Currently on list? (*):  no 
Submitted:  10/4/2004 11:38:13 CDT 
Last modified:  10/4/2004 11:38:13 CDT 
Database id:  71838 
Status Flags:  Verify 
Score (*):  29.8666 (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.
 Mersenne cofactor (archivable *)
 Prime on list: no, rank 22
Subcategory: "Mersenne cofactor"
(archival tag id 195460, tag last modified 20180404 21:20:32)  Elliptic Curve Primality Proof (archivable *)
 Prime on list: no, rank 440
Subcategory: "ECPP"
(archival tag id 195459, tag last modified 20180702 08:50:19)
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  71838 
person_id  9 
machine  Linux P4 2.8GHz 
what  prp 
notes  Command: /home/caldwell/client/pfgw f tc q"(2^145611)/8074991336582835391" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (2^145611)/8074991336582835391 [N1/N+1, BrillhartLehmerSelfridge] trial factoring to 1169910 Running N1 test using base 13 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1792,21) to FFT(1792,20) Reduced from FFT(1792,20) to FFT(1792,19) Reduced from FFT(1792,19) to FFT(1792,18) Reduced from FFT(1792,18) to FFT(1792,17) 29006 bit request FFT size=(1792,17) Running N+1 test using discriminant 31, base 17+sqrt(31) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1792,21) to FFT(1792,20) Reduced from FFT(1792,20) to FFT(1792,19) Reduced from FFT(1792,19) to FFT(1792,18) Reduced from FFT(1792,18) to FFT(1792,17) 29014 bit request FFT size=(1792,17) Calling N1 BLS with factored part 0.19% and helper 0.03% (0.63% proof) (2^145611)/8074991336582835391 is Fermat and Lucas PRP! (15.0542s+0.0211s)

modified  20041120 19:47:49 
created  20041004 11:53:00 
id  76832 

Query times: 0.0004 seconds to select prime, 0.0009 seconds to seek comments.
