# 5256037# + 1

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: | 5256037# + 1 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Primorial |

Proof-code(s): (*): | p444 : Kadowaki, MultiSieve, PrimeGrid, PRST, OpenPFGW |

Decimal Digits: | 2281955 (log_{10} is 2281954.8287246) |

Rank (*): | 230 (digit rank is 1) |

Entrance Rank (*): | 210 |

Currently on list? (*): | short |

Submitted: | 8/9/2024 23:02:22 UTC |

Last modified: | 8/31/2024 23:37:16 UTC |

Database id: | 138394 |

Status Flags: | none |

Score (*): | 49.1629 (normalized score 59.5531) |

#### 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.

#### 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 138394 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"5256037#+1" >command_output 2>&1

PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]

Primality testing 5256037#+1 [N-1, Brillhart-Lehmer-Selfridge]

trial

Running N-1 test using base 2

Generic modular reduction using generic reduction FMA3 FFT length 768K, Pass1=384, Pass2=2K, clm=2 on A 7580490-bit number

Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate

Iteration: 7737246/50354430 ERROR: ROUND OFF 0.4636>0.45

(Test aborted, try again using the -a1 switch)

Running N-1 test using base 3

Generic modular reduction using generic reduction FMA3 FFT length 800K, Pass1=320, Pass2=2560, clm=2 on A 7580490-bit number

Calling Brillhart-Lehmer-Selfridge with factored part 33.33%

5256037#+1 is prime! (1872278.6805s+11.5610s)

[Elapsed time: 21.67 days]modified 2024-08-31 23:33:42 created 2024-08-10 07:28:51 id 184236

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.

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