E(1468)/(95 · 217158949445380764696306893 · 597712879321361736404369071)
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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:E(1468)/(95 · 217158949445380764696306893 · 597712879321361736404369071)
Verification status (*):PRP
Official Comment:Euler irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c4 : Broadhurst, Primo
Decimal Digits:3671   (log10 is 3670.30196446)
Rank (*):83625 (digit rank is 2)
Entrance Rank (*):32760
Currently on list? (*):short
Submitted:12/21/2003 12:31:51 CDT
Last modified:12/21/2003 12:31:51 CDT
Database id:67770
Blob database id:107
Status Flags:Verify
Score (*):29.328 (normalized score 0)

Description: (from blob table id=107)

[This prime has a pre-calculated decimal expansion (linked blob)]

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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 498
Subcategory: "ECPP"
(archival tag id 179005, tag last modified 2017-11-27 10:20:19)
Euler Irregular primes (archivable *)
Prime on list: yes, rank 10
Subcategory: "Euler Irregular primes"
(archival tag id 179004, tag last modified 2014-06-21 13:51:45)

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_id67770
person_id9
machineLinux P4 2.8GHz
whatprp
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 2004308000...5156200481 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 969046
Running N-1 test using base 3
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(1536,21) to FFT(1536,20)
Reduced from FFT(1536,20) to FFT(1536,19)
Reduced from FFT(1536,19) to FFT(1536,18)
Reduced from FFT(1536,18) to FFT(1536,17)
Reduced from FFT(1536,17) to FFT(1536,16)
24394 bit request FFT size=(1536,16)
Running N+1 test using discriminant 7, base 1+sqrt(7)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(1536,21) to FFT(1536,20)
Reduced from FFT(1536,20) to FFT(1536,19)
Reduced from FFT(1536,19) to FFT(1536,18)
Reduced from FFT(1536,18) to FFT(1536,17)
Reduced from FFT(1536,17) to FFT(1536,16)
24402 bit request FFT size=(1536,16)
Running N+1 test using discriminant 7, base 2+sqrt(7)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(1536,21) to FFT(1536,20)
Reduced from FFT(1536,20) to FFT(1536,19)
Reduced from FFT(1536,19) to FFT(1536,18)
Reduced from FFT(1536,18) to FFT(1536,17)
Reduced from FFT(1536,17) to FFT(1536,16)
24402 bit request FFT size=(1536,16)
Calling N-1 BLS with factored part 0.25% and helper 0.03% (0.79% proof)
2004308000...5156200481 is Fermat and Lucas PRP! (13.1723s+0.0017s)
modified2004-08-21 09:24:31
created2004-08-21 09:24:17
id76340

Query times: 0.0006 seconds to select prime, 0.0007 seconds to seek comments.