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# Phi(3, 10^{160048}) + (137 · 10^{160049} + 731 · 10^{157453}) · (10^{2595} - 1)/999

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: | Phi(3, 10^{160048}) + (137 · 10^{160049} + 731 · 10^{157453}) · (10^{2595} - 1)/999 |
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Verification status (*): | Proven |

Official Comment (*): | Palindrome |

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

Proof-code(s): (*): | p44 : Broadhurst, OpenPFGW |

Decimal Digits: | 320097 (log_{10} is 320096) |

Rank (*): | 19286 (digit rank is 1) |

Entrance Rank (*): | 5855 |

Currently on list? (*): | short |

Submitted: | 3/8/2014 22:48:53 UTC |

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

Database id: | 117386 |

Status Flags: | TrialDiv |

Score (*): | 43.1346 (normalized score 0.1956) |

#### 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.

- Palindrome (archivable *)
- Prime on list:
yes, rank11

Subcategory: "Palindrome"

(archival tag id 217639, tag last modified 2023-03-11 15:53:59)

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

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#### 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 117386 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -tc -q"Phi(3,10^160048)+(137*10^160049+731*10^157453)*(10^2595-1)/999" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing Phi(3,10^160048)+(137*10^160049+731*10^157453)*(10^2595-1)/999 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Running N-1 test using base 23 Running N+1 test using discriminant 31, base 10+sqrt(31) Calling N-1 BLS with factored part 49.19% and helper 0.00% (147.57% proof) Phi(3,10^160048)+(137*10^160049+731*10^157453)*(10^2595-1)/999 is prime! (87546.8156s+0.1862s) [Elapsed time: 24.32 hours] modified 2020-07-07 22:30:17 created 2014-03-08 22:53:01 id 162905

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.

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