CM a fast ECPP implementation Andreas Enge

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):	CH14
Active wild codes:	^E\d+
Code prefix:	E
E-mail address:	andreas.enge@inria.fr
Web page:	https://www.multiprecision.org/cm/
Username	cm	(entry created on 5/12/2022 07:17:51 UTC)
Database id:	5485	(entry last modified on 11/16/2023 16:29:29 UTC)
Program Does *:	general
Active primes:	on current list: 80, rank by number 12
Total primes:	number ever on any list: 94
Production score:	for current list 41 (normalized: 0), total 41.0808, rank by score 30
Largest prime:	(102936²¹⁹⁶¹ - 1)/102935 ‏(‎110076 digits) via code CH14 on 11/17/2023 14:15:40 UTC
Most recent:	V(183089) ‏(‎38264 digits) via code E4 on 12/1/2023 20:56:05 UTC
Entrance Rank:	mean 67711.23 (minimum 45313, maximum 75522)

Descriptive Data: (report abuse)

CM, a software for complex multiplication of elliptic curves, also implements the fastECPP algorithm due to Morain, Franke, Kleinjung and Wirth. It is available under the GPL version 3 or later at

https://www.multiprecision.org/cm/

It relies on the approach of computing class polynomials by complex approximations. Optimal class invariants are chosen derived from Weber functions, simple or double eta quotients, including cases where it is enough to compute lower-degree subfields of the class field. The evaluation of modular functions, which is the most important part of the class polynomial computation, has been optimised. To ease the step of factoring class polynomials modulo primes, the class fields are then represented as a tower of cyclic Galois extensions of prime degree.

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

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