
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:  2840178 · Bern(1870)/85 
Verification status (*):  PRP 
Official Comment:  Irregular, ECPP 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  c8 : Water, Broadhurst, Primo 
Decimal Digits:  3821 (log_{10} is 3820.47675595) 
Rank (*):  83154 (digit rank is 1) 
Entrance Rank (*):  32314 
Currently on list? (*):  short 
Submitted:  12/2/2003 20:49:03 CDT 
Last modified:  12/2/2003 20:49:03 CDT 
Database id:  67526 
Status Flags:  Verify 
Score (*):  29.4528 (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 15
Subcategory: "Irregular Primes"
(archival tag id 178452, tag last modified 20161118 02:20:40)  Elliptic Curve Primality Proof (archivable *)
 Prime on list: no, rank 479
Subcategory: "ECPP"
(archival tag id 178453, tag last modified 20170709 21:50:21)
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  67526 
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 2997477656...5776579313 [N1/N+1, BrillhartLehmerSelfridge] trial factoring to 1012270 Running N1 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) 25392 bit request FFT size=(1536,17) Running N+1 test using discriminant 11, base 1+sqrt(11) 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) 25400 bit request FFT size=(1536,17) Calling N+1 BLS with factored part 0.23% and helper 0.09% (0.77% proof) 2997477656...5776579313 is Fermat and Lucas PRP! (11.0226s+0.0018s)

modified  20031202 20:53:13 
created  20031202 20:53:02 
id  72462 

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