Note 2023 is the last year that I will maintain this site--there is currently no plan to continue it after that.

John Renze's Coppersmith-Howgrave-Graham PARI script

A titan, as defined by Samuel Yates, is anyone who has found a titanic prime. This page provides data on those that have found these primes. The data below only reflects on the primes currently on the list. (Many of the terms that are used here are explained on another page.)

Proof-code(s):

CH1, CH2, CH3, CH4, CH5, CH6, CH7, CH8, CH9, CH10, CH11, CH12, CH13

Code prefix:

E-mail address:

jrenze

(at)

yahoo

(dot)

com

Username

CHG

(entry created on 9/11/2005 07:15:40 CDT)

Database id:

797

(entry last modified on 9/10/2021 17:11:02 CDT)

Program Does *:

classical

Active primes:

on current list: 26, rank by number 22

Total primes:

number ever on any list: 76

Production score:

for current list 48 (normalized: 32), total 48.1732, rank by score 25

Largest prime:

3^2120580 - 3⁶²³⁸¹⁶ - 1 ‏(‎1011774 digits) via code CH9 on 5/12/2019 08:20:20 CDT

Most recent:

3^1681130 + 3⁴⁴⁵⁷⁸¹ + 1 ‏(‎802103 digits) via code CH9 on 9/1/2022 17:58:33 CDT

Entrance Rank:

mean 30961.96 (minimum 414, maximum 62608)

Descriptive Data: (report abuse)

A script which implements the lattice basis reduction methods of Coppersmith and Howgrave-Graham to search for divisors in residue classes. This is useful when a BLS test with a factorization percentage of more than 25% has been run. The script is available at the primeform e-mail group, under "CHG.GP."

Factorization percentage record: 26.14% by Broadhurst, Renze, and de Water (December 2005)

Surname: CHG (used for alphabetizing and in codes).
Unverified primes are omitted from counts and lists until verification completed.

I administer John Renze's Coppersmith-Howgrave-Graham PARI script and I would like to