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# (2^{42737} + 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.

#### This prime's information:

Description: | (2^{42737} + 1)/3 |
---|---|

Verification status (*): | PRP |

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

Unofficial Comments: | This prime has 1 user comment below. |

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

Decimal Digits: | 12865 (log_{10} is 12864.641803437) |

Rank (*): | 77651 (digit rank is 1) |

Entrance Rank (*): | 32933 |

Currently on list? (*): | short |

Submitted: | 8/28/2007 18:19:44 UTC |

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

Database id: | 82071 |

Status Flags: | Verify |

Score (*): | 33.2205 (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.

- Elliptic Curve Primality Proof (archivable *)
- Prime on list:
no, rank190

Subcategory: "ECPP"

(archival tag id 193533, tag last modified 2023-03-11 16:02:30)- Generalized Lucas Number (archivable *)
- Prime on list:
no, rank38

Subcategory: "Generalized Lucas Number"

(archival tag id 193532, tag last modified 2023-03-11 16:02:31)- Wagstaff (archivable *)
- Prime on list:
yes, rank5

Subcategory: "Wagstaff"

(archival tag id 193534, tag last modified 2023-03-11 16:02:31)

#### User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

#### 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 82071 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"(2^42737+1)/3" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (2^42737+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 7 Running N-1 test using base 13 Running N-1 test using base 19 Running N+1 test using discriminant 29, base 2+sqrt(29) Running N+1 test using discriminant 29, base 3+sqrt(29) Running N+1 test using discriminant 29, base 5+sqrt(29) Running N+1 test using discriminant 29, base 6+sqrt(29) Running N+1 test using discriminant 29, base 8+sqrt(29) Running N+1 test using discriminant 29, base 9+sqrt(29) Calling N+1 BLS with factored part 0.98% and helper 0.15% (3.08% proof) (2^42737+1)/3 is Fermat and Lucas PRP! (414.8100s+0.0000s) [Elapsed time: 6.98333333333333 minutes] modified 2020-07-07 22:30:40 created 2007-08-28 18:20:30 id 93262

field value prime_id 82071 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"(2^42737+1)/3" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 3771838 (2^42737+1)/3 has no small factor. [Elapsed time: 4.875 seconds] modified 2020-07-07 22:30:40 created 2007-08-28 18:22:01 id 93263

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.

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