# (10^{2332974} + 1)^{2} - 2

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: | (10^{2332974} + 1)^{2} - 2 |
---|---|

Verification status (*): | Proven |

Official Comment (*): | [none] |

Proof-code(s): (*): | p405 : Propper, Cksieve, OpenPFGW |

Decimal Digits: | 4665949 (log_{10} is 4665948) |

Rank (*): | 48 (digit rank is 1) |

Entrance Rank (*): | 48 |

Currently on list? (*): | short |

Submitted: | 2/20/2024 13:05:54 UTC |

Last modified: | 3/29/2024 14:37:18 UTC |

Database id: | 137497 |

Status Flags: | none |

Score (*): | 51.3538 (normalized score 563.0463) |

#### 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 137497 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"(10^2332974+1)^2-2" >command_output 2>&1

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

Primality testing (10^2332974+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]

trial

Running N-1 test using base 7

Generic modular reduction using generic reduction FMA3 FFT length 1600K, Pass1=640, Pass2=2560, clm=1 on A 15499944-bit number

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

Generic modular reduction using generic reduction FMA3 FFT length 1600K, Pass1=640, Pass2=2560, clm=1 on A 15499944-bit number

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

Iteration: 39/15499951 ERROR: ROUND OFF 0.5>0.45

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

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

Generic modular reduction using generic reduction FMA3 FFT length 1680K, Pass1=448, Pass2=3840, clm=2 on A 15499944-bit number

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

Iteration: 947/15499951 ERROR: ROUND OFF 0.48438>0.45

(Test aborted, try again using the -a2 (or possibly -a0) switch)

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

Generic modular reduction using generic reduction FMA3 FFT length 1728K, Pass1=768, Pass2=2304, clm=1 on A 15499944-bit number

Running N+1 test using discriminant 13, base 2+sqrt(13)

Generic modular reduction using generic reduction FMA3 FFT length 1600K, Pass1=640, Pass2=2560, clm=1 on A 15499944-bit number

Calling N+1 BLS with factored part 50.00% and helper 0.00% (150.00% proof)

(10^2332974+1)^2-2 is prime! (3269692.5325s+0.0728s)

[Elapsed time: 37.84 days]modified 2024-03-29 13:40:35 created 2024-02-20 17:25:37 id 183339

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

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