# 652229318541 · 3527# + 3399421517

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: | 652229318541 · 3527# + 3399421517 |
---|---|

Verification status (*): | PRP |

Official Comment (*): | Consecutive primes arithmetic progression (1,d=30), ECPP |

Proof-code(s): (*): | c98 : Batalov, EMsieve, Primo |

Decimal Digits: | 1504 (log_{10} is 1503.1618504971) |

Rank (*): | 104321 (digit rank is 11) |

Entrance Rank (*): | 104289 |

Currently on list? (*): | no |

Submitted: | 10/12/2021 20:36:03 CDT |

Last modified: | 10/12/2021 21:37:18 CDT |

Database id: | 132828 |

Status Flags: | Verify, TrialDiv |

Score (*): | 26.546 (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.

- Consecutive Primes in Arithmetic Progression (archivable class *)
- Prime on list:
no, rank56

Subcategory: "Consecutive primes in arithmetic progression (1,d=*)"

(archival tag id 226383, tag last modified 2021-10-14 15:37:18)- Arithmetic Progressions of Primes (archivable class *)
- Prime on list:
no, rank895

Subcategory: "Arithmetic progression (1,d=*)"

(archival tag id 226384, tag last modified 2021-10-14 15:37:17)- Elliptic Curve Primality Proof (archivable *)
- Prime on list:
no, rank886

Subcategory: "ECPP"

(archival tag id 226385, tag last modified 2021-10-14 15:37:18)

#### 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 132828 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"652229318541*3527#+3399421517" 2>&1

PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 652229318541*3527#+3399421517 [N-1/N+1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 5

Running N+1 test using discriminant 13, base 1+sqrt(13)

Calling N+1 BLS with factored part 0.52% and helper 0.02% (1.58% proof)

652229318541*3527#+3399421517 is Fermat and Lucas PRP! (0.1366s+0.0005s)

[Elapsed time: 0.00 seconds]modified 2021-10-12 20:41:01 created 2021-10-12 20:41:01 id 178541

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

Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.