# - E(2762)/2670541

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: 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:

Description: | - E(2762)/2670541 |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Euler irregular, ECPP |

Proof-code(s): (*): | c11 : Oakes, Primo |

Decimal Digits: | 7760 (log_{10} is 7759.25335463) |

Rank (*): | 84810 (digit rank is 1) |

Entrance Rank (*): | 27474 |

Currently on list? (*): | short |

Submitted: | 7/21/2004 11:13:29 UTC |

Last modified: | 3/11/2023 15:54:10 UTC |

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, rank9

Subcategory: "Euler Irregular primes"

(archival tag id 194531, tag last modified 2023-10-06 17:37:13)- Elliptic Curve Primality Proof (archivable *)
- Prime on list:
no, rank401

Subcategory: "ECPP"

(archival tag id 194532, tag last modified 2023-12-16 03:37:31)

#### 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 [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) modified 2020-07-07 22:30:45 created 2004-08-09 15:34:44 id 76215

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.

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