# (2^{95369} + 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^{95369} + 1)/3 |
---|---|

Verification status (*): | PRP |

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

Proof-code(s): (*): | x49 : Facq, Asuncion, Allombert, Unknown |

Decimal Digits: | 28709 (log_{10} is 28708.452535223) |

Rank (*): | 65145 (digit rank is 1) |

Entrance Rank (*): | 64979 |

Currently on list? (*): | short |

Submitted: | 8/3/2021 03:07:06 CDT |

Last modified: | 8/3/2021 03:37:31 CDT |

Database id: | 132583 |

Status Flags: | Verify, TrialDiv |

Score (*): | 35.7037 (normalized score 0.0001) |

#### 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:
yes, rank9

Subcategory: "Generalized Lucas Number"

(archival tag id 226235, tag last modified 2021-08-03 03:37:35)- Elliptic Curve Primality Proof (archivable *)
- Prime on list:
yes, rank9

Subcategory: "ECPP"

(archival tag id 226236, tag last modified 2021-09-18 09:37:41)- Wagstaff (archivable *)
- Prime on list:
yes, rank1

Subcategory: "Wagstaff"

(archival tag id 226237, tag last modified 2021-08-03 03:37:36)

#### 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 132583 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"(2^95369+1)/3" 2>&1

PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing (2^95369+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 discriminant 13, base 1+sqrt(13)

Calling N-1 BLS with factored part 0.50% and helper 0.05% (1.56% proof)

(2^95369+1)/3 is Fermat and Lucas PRP! (13.3551s+0.0667s)

[Elapsed time: 14.00 seconds]modified 2021-08-03 03:11:15 created 2021-08-03 03:11:01 id 178295

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

Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.