
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(1736)/(55695515 · 75284987831 · 3222089324971117) 
Verification status (*):  PRP 
Official Comment:  Euler irregular, ECPP 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  c4 : Broadhurst, Primo 
Decimal Digits:  4498 (log_{10} is 4497.45211785) 
Rank (*):  83669 (digit rank is 1) 
Entrance Rank (*):  31911 
Currently on list? (*):  short 
Submitted:  1/10/2004 21:55:03 CDT 
Last modified:  1/10/2004 21:55:03 CDT 
Database id:  68041 
Blob database id:  106 
Status Flags:  Verify 
Score (*):  29.96 (normalized score 0) 

Description:
(from blob table id=106)
[This prime has a precalculated 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.
 Euler Irregular primes (archivable *)
 Prime on list: yes, rank 9
Subcategory: "Euler Irregular primes"
(archival tag id 195422, tag last modified 20180314 05:50:22)  Elliptic Curve Primality Proof (archivable *)
 Prime on list: no, rank 421
Subcategory: "ECPP"
(archival tag id 195423, tag last modified 20180423 04:20:12)
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  68041 
person_id  9 
machine  Linux P4 2.8GHz 
what  prp 
notes  PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2832160403...7135736289 [N1/N+1, BrillhartLehmerSelfridge] trial factoring to 1208717 Running N1 test using base 3 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) 29890 bit request FFT size=(1792,17) Running N+1 test using discriminant 17, base 8+sqrt(17) 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) 29898 bit request FFT size=(1792,17) Running N+1 test using discriminant 17, base 10+sqrt(17) 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) 29898 bit request FFT size=(1792,17) Calling N+1 BLS with factored part 0.19% and helper 0.15% (0.74% proof) 2832160403...7135736289 is Fermat and Lucas PRP! (54.5075s+0.0022s)

modified  20040116 11:28:17 
created  20040116 11:27:23 
id  73298 

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.
