6 · Bern(4306)/2153
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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:6 · Bern(4306)/2153
Verification status (*):PRP
Official Comment:Irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):FE8 : Oakes, Morain, Water, Broadhurst, FastECPP
Decimal Digits:10342   (log10 is 10341.250474092)
Rank (*):72283 (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 5
Subcategory: "Irregular Primes"
(archival tag id 208962, tag last modified 2014-02-12 12:52:14)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 140
Subcategory: "ECPP"
(archival tag id 208963, tag last modified 2017-06-06 13:20:22)

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_id87451
person_id9
machineRedHat P4 P4
whattrial_divided
notesPFGW 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]
modified2011-12-27 16:48:44
created2009-04-04 12:18:13
id104267

fieldvalue
prime_id87451
person_id9
machineDitto P4 P4
whatprp
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 1780221704...5593370631 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 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]
modified2009-04-04 12:47:15
created2009-04-04 12:46:28
id104270

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.