# 40931485 · 2^{53124} - 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: | 40931485 · 2^{53124} - 3 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | Cunningham chain 2nd kind (2p-1) |

Proof-code(s): (*): | p222 : Underbakke, TwinGen, LLR, OpenPFGW |

Decimal Digits: | 16000 (log_{10} is 15999.529547155) |

Rank (*): | 71287 (digit rank is 1) |

Entrance Rank (*): | 27214 |

Currently on list? (*): | no |

Submitted: | 3/1/2007 10:22:33 CDT |

Last modified: | 3/3/2007 15:29:06 CDT |

Database id: | 79587 |

Status Flags: | none |

Score (*): | 33.8957 (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.

- Cunningham Chains (2nd kind) (archivable class *)
- Prime on list:
no, rank23, weight 33.617907706275

Subcategory: "Cunningham chain 2nd kind (2p-1)"

(archival tag id 212417, tag last modified 2020-06-02 14:12:08)

#### 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 79587 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 40931485 2 53124 -3 2>&1 [Elapsed time: 8.219 seconds] modified 2020-07-07 17:30:41 created 2007-03-01 10:52:01 id 88283

field value prime_id 79587 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -tc -hhelper_file_id_79587 -q"40931485*2^53124-3" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 40931485*2^53124-3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_file_id_79587 Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) 106308 bit request FFT size=(6144,18) Running N+1 test using discriminant 5, base 4+sqrt(5) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) 106316 bit request FFT size=(6144,18) Running N+1 test using discriminant 5, base 5+sqrt(5) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) 106316 bit request FFT size=(6144,18) Calling N+1 BLS with factored part 100.00% and helper 0.08% (300.09% proof) 40931485*2^53124-3 is prime! (197.1100s+0.0000s) [Elapsed time: 199 seconds] Helper file contains: "40931485*2^53123-1" modified 2020-07-07 17:30:41 created 2007-03-03 15:25:47 id 88327

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.

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