
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:  6 · Bern(4306)/2153 
Verification status (*):  PRP 
Official Comment:  Irregular, ECPP 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  FE8 : Oakes, Morain, Water, Broadhurst, FastECPP 
Decimal Digits:  10342 (log_{10} is 10341.250474092) 
Rank (*):  73599 (digit rank is 1) 
Entrance Rank (*):  40519 
Currently on list? (*):  short 
Submitted:  4/4/2009 12:16:15 CDT 
Last modified:  4/4/2009 12:50:40 CDT 
Database id:  87451 
Status Flags:  Verify 
Score (*):  32.5441 (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.
 Irregular Primes (archivable *)
 Prime on list: yes, rank 6
Subcategory: "Irregular Primes"
(archival tag id 208962, tag last modified 20180423 04:20:13)  Elliptic Curve Primality Proof (archivable *)
 Prime on list: no, rank 160
Subcategory: "ECPP"
(archival tag id 208963, tag last modified 20180922 16:20:28)
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  87451 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] 1780221704...9703946799.........1062015654039575 1/1
trial factoring to 2979440 1780221704...5593370631 has no small factor. [Elapsed time: 12.441 seconds]

modified  20111227 16:48:44 
created  20090404 12:18:13 
id  104267 

field  value 
prime_id  87451 
person_id  9 
machine  Ditto P4 P4 
what  prp 
notes  PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 1780221704...5593370631 [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(4096,21) to FFT(4096,20) Reduced from FFT(4096,20) to FFT(4096,19) Reduced from FFT(4096,19) to FFT(4096,18) Reduced from FFT(4096,18) to FFT(4096,17) 68714 bit request FFT size=(4096,17) Running N+1 test using discriminant 13, base 1+sqrt(13) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(4096,21) to FFT(4096,20) Reduced from FFT(4096,20) to FFT(4096,19) Reduced from FFT(4096,19) to FFT(4096,18) Reduced from FFT(4096,18) to FFT(4096,17) 68722 bit request FFT size=(4096,17) Calling N+1 BLS with factored part 0.10% and helper 0.09% (0.41% proof) 1780221704...5593370631 is Fermat and Lucas PRP! (46.5600s+0.0100s) [Elapsed time: 47.00 seconds]

modified  20090404 12:47:15 
created  20090404 12:46:28 
id  104270 

Query times: 0.0005 seconds to select prime, 0.0008 seconds to seek comments.
