# ((((((2521008887^{3} + 80)^{3} + 12)^{3} + 450)^{3} + 894)^{3} + 3636)^{3} + 70756)^{3} + 97220

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: | ((((((2521008887^{3} + 80)^{3} + 12)^{3} + 450)^{3} + 894)^{3} + 3636)^{3} + 70756)^{3} + 97220 |
---|---|

Verification status (*): | PRP |

Official Comment (*): | ECPP, Mills' prime |

Unofficial Comments: | This prime has 2 user comments below. |

Proof-code(s): (*): | FE1 : Morain, FastECPP |

Decimal Digits: | 20562 (log_{10} is 20561.24316172) |

Rank (*): | 71598 (digit rank is 1) |

Entrance Rank (*): | 22561 |

Currently on list? (*): | no |

Submitted: | 6/5/2006 20:32:01 UTC |

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

Database id: | 77907 |

Status Flags: | Verify |

Score (*): | 34.6719 (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.

- Mills' prime (tolerated *)
- Prime on list:
no, rank1

Subcategory: "Mills' prime"

(archival tag id 192157, tag last modified 2023-03-11 15:53:59)- Elliptic Curve Primality Proof (archivable *)
- Prime on list:
no, rank73

Subcategory: "ECPP"

(archival tag id 192156, tag last modified 2023-09-17 09:37:11)

#### 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 77907 person_id 9 machine WinXP P4 2.2GHz By K what prp notes Command: pfgw.exe -n -f -tc -q"(((((((2521008881+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220" 2>&1 PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing (((((((2521008881+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 6252599 Running N-1 test using base 3 Running N-1 test using base 5 Running N-1 test using base 11 Running N+1 test using discriminant 19, base 1+sqrt(19) Calling N-1 BLS with factored part 0.05% and helper 0.03% (0.17% proof) (((((((2521008881+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220 is Fermat and Lucas PRP! (351.7329s+0.0394s) [Elapsed time: 356 seconds] modified 2020-07-07 22:30:42 created 2006-06-05 20:58:09 id 84439

field value prime_id 77907 person_id 9 machine GenToo P3 400MHz what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"((((((2521008887^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] ((((((2521008887^3+80)^3+.........^3+3636)^3+70756 1/1 trial factoring to 6252599 ((((((2521008887^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220 has no small factor. [Elapsed time: 10.931 seconds] modified 2020-07-07 22:30:42 created 2006-07-07 15:39:24 id 85237

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.

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