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, p441
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 7/18/2024 23:51:20 UTC)
Program Does *:	general
Active primes:	on current list: 110, rank by number 12
Total primes:	number ever on any list: 127
Production score:	for current list 41 (normalized: 0), total 41.8958, rank by score 31
Largest prime:	(124750²⁷⁷⁵¹ - 1)/124749 ‏(‎141416 digits) via code p441 on 9/25/2024 20:49:39 UTC
Most recent:	2¹³⁹⁹⁶⁴ + 35461 ‏(‎42134 digits) via code E11 on 10/26/2024 20:28:51 UTC
Entrance Rank:	mean 68422.29 (minimum 43273, maximum 79478)

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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