- E(2762)/2670541
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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(2762)/2670541
Verification status (*):PRP
Official Comment:Euler irregular, ECPP
Proof-code(s): (*):c11 : Oakes, Primo
Decimal Digits:7760   (log10 is 7759.25335463)
Rank (*):75151 (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 2
Subcategory: "Euler Irregular primes"
(archival tag id 194531, tag last modified 2014-06-21 13:51:45)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 236
Subcategory: "ECPP"
(archival tag id 194532, tag last modified 2017-10-14 12:20:21)

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_id71007
person_id9
machineLinux P4 2.8GHz
whatprp
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 1792068587...3618040061 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 2183709
Running N-1 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 N-1 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 N-1 BLS with factored part 0.20% and helper 0.09% (0.69% proof)
1792068587...3618040061 is Fermat and Lucas PRP! (44.2903s+0.0687s)
modified2004-08-09 10:35:29
created2004-08-09 10:34:44
id76215

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.