(214561 - 1)/8074991336582835391
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help
 

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:(214561 - 1)/8074991336582835391
Verification status (*):PRP
Official Comment:Mersenne cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c8 : Water, Broadhurst, Primo
Decimal Digits:4365   (log10 is 4364.3906248)
Rank (*):82524 (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 21
Subcategory: "Mersenne cofactor"
(archival tag id 195460, tag last modified 2017-10-19 05:50:26)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 426
Subcategory: "ECPP"
(archival tag id 195459, tag last modified 2017-11-16 23:50:19)

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.

David Broadhurst writes (11 Sep 2014): 
certificate

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_id71838
person_id9
machineLinux P4 2.8GHz
whatprp
notesCommand: /home/caldwell/client/pfgw -f -tc -q"(2^14561-1)/8074991336582835391" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing (2^14561-1)/8074991336582835391 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 1169910
Running N-1 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 N-1 BLS with factored part 0.19% and helper 0.03% (0.63% proof)
(2^14561-1)/8074991336582835391 is Fermat and Lucas PRP! (15.0542s+0.0211s)
modified2004-11-20 19:47:49
created2004-10-04 11:53:00
id76832

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.