# 31723 · 2^{1398273} - 507567

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: | 31723 · 2^{1398273} - 507567 |
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Verification status (*): | Proven |

Official Comment (*): | [none] |

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

Proof-code(s): (*): | p363 : Batalov, OpenPFGW |

Decimal Digits: | 420927 (log_{10} is 420926.61650131) |

Rank (*): | 9524 (digit rank is 2) |

Entrance Rank (*): | 1070 |

Currently on list? (*): | no |

Submitted: | 9/6/2013 14:11:39 CDT |

Last modified: | 10/4/2013 13:02:05 CDT |

Removed (*): | 3/17/2019 07:32:19 CDT |

Database id: | 115395 |

Status Flags: | TrialDiv |

Score (*): | 43.9762 (normalized score 0.5184) |

#### 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 115395 person_id 9 machine WinXP Dual Core 2.6GHz 32-bit what prime notes Command: pfgw32.exe -tc -hhelp.txt -q"31723*2^1398273-507567" 2>&1 PFGW Version 3.7.3.32BIT.20130210.Win_Dev [GWNUM 27.8] Primality testing 31723*2^1398273-507567 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file help.txt Sieve re-allocated with a limit of 400000000000. Running N-1 test using base 3 Running N-1 test using base 13 Running N+1 test using discriminant 19, base 2+sqrt(19) Calling N-1 BLS with factored part 100.00% and helper 0.00% (300.00% proof) 31723*2^1398273-507567 is prime! (133555.7758s+0.0035s) [Elapsed time: 133553 seconds] Helper File: 2^1398269-1 modified 2020-07-07 17:30:18 created 2013-09-10 10:15:54 id 160939

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

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