
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(2762)/2670541 
Verification status (*):  PRP 
Official Comment:  Euler irregular, ECPP 
Proofcode(s): (*):  c11 : Oakes, Primo 
Decimal Digits:  7760 (log_{10} is 7759.25335463) 
Rank (*):  76947 (digit rank is 1) 
Entrance Rank (*):  27474 
Currently on list? (*):  short 
Submitted:  7/21/2004 06:13:29 CDT 
Last modified:  7/21/2004 06:13:29 CDT 
Database id:  71007 
Blob database id:  125 
Status Flags:  Verify 
Score (*):  31.6534 (normalized score 0) 

Description:
(from blob table id=125)
Pari code:
nm=1400;eul=vector(nm);
{for(n=1,nm,r=1;s=  1;
for(k=1,n  1,r=r * (2 * n  2 * k + 2) * (2 * n  2 * k + 1)/(2 * k * (2 * k  1));
s=s  eul[k] * r);eul[n]=s)}
E(n)=eul[n/2];
print(  E(2762)/(101 * 137 * 193));
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 3
Subcategory: "Euler Irregular primes"
(archival tag id 194531, tag last modified 20180314 05:50:22)  Elliptic Curve Primality Proof (archivable *)
 Prime on list: no, rank 269
Subcategory: "ECPP"
(archival tag id 194532, tag last modified 20190407 01:20:26)
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  71007 
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 1792068587...3618040061 [N1/N+1, BrillhartLehmerSelfridge] trial factoring to 2183709 Running N1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3072,21) to FFT(3072,20) Reduced from FFT(3072,20) to FFT(3072,19) Reduced from FFT(3072,19) to FFT(3072,18) Reduced from FFT(3072,18) to FFT(3072,17) 51560 bit request FFT size=(3072,17) Running N1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3072,21) to FFT(3072,20) Reduced from FFT(3072,20) to FFT(3072,19) Reduced from FFT(3072,19) to FFT(3072,18) Reduced from FFT(3072,18) to FFT(3072,17) 51560 bit request FFT size=(3072,17) Running N+1 test using discriminant 29, base 1+sqrt(29) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3072,21) to FFT(3072,20) Reduced from FFT(3072,20) to FFT(3072,19) Reduced from FFT(3072,19) to FFT(3072,18) Reduced from FFT(3072,18) to FFT(3072,17) 51568 bit request FFT size=(3072,17) Calling N1 BLS with factored part 0.20% and helper 0.09% (0.69% proof) 1792068587...3618040061 is Fermat and Lucas PRP! (44.2903s+0.0687s)

modified  20040809 10:35:29 
created  20040809 10:34:44 
id  76215 

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
