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# (2^{3539} + 1)/3

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.

Description: | (2^{3539} + 1)/3 |
---|---|

Verification status (*): | PRP |

Official Comment (*): | First titanic by ECPP, generalized Lucas number, Wagstaff |

Proof-code(s): (*): | M : Morain |

Decimal Digits: | 1065 (log_{10} is 1064.86803340011) |

Rank (*): | 118374 (digit rank is 8) |

Entrance Rank (*): | 838 |

Currently on list? (*): | short |

Submitted: | 1989 |

Last modified: | 1989 |

Database id: | 54344 |

Status Flags: | Verify |

Score (*): | 25.4686 (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.

- Generalized Lucas Number (archivable *)
- Prime on list:
no, rank108

Subcategory: "Generalized Lucas Number"

(archival tag id 181330, tag last modified 2020-05-28 13:20:28)- * old special cases (deprecated *)
- Prime on list:
no, rank1

Subcategory: "* old special cases"

(archival tag id 181329, tag last modified 2005-06-03 13:39:34)- Elliptic Curve Primality Proof (archivable *)
- Prime on list:
no, rank946

Subcategory: "ECPP"

(archival tag id 181331, tag last modified 2020-06-22 13:50:28)- Wagstaff (archivable *)
- Prime on list:
yes, rank9

Subcategory: "Wagstaff"

(archival tag id 181332, tag last modified 2014-09-17 12:50:33)

#### 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 54344 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing (2^3539+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 13, base 1+sqrt(13) Running N+1 test using discriminant 13, base 2+sqrt(13) Running N+1 test using discriminant 13, base 3+sqrt(13) Running N+1 test using discriminant 13, base 6+sqrt(13) Running N+1 test using discriminant 13, base 8+sqrt(13) Calling N+1 BLS with factored part 2.69% and helper 1.33% (9.44% proof) (2^3539+1)/3 is Fermat and Lucas PRP! (46.500000 seconds) modified 2003-03-25 11:23:04 created 2003-01-03 23:43:33 id 60765

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

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