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:
Web page:
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: 90, rank by number 12
Total primes: number ever on any list: 105
Production score: for current list 41 (normalized: 0), total 41.4458, rank by score 30
Largest prime: (9236524691 - 1)/92364 ‏(‎122599 digits) via code CH14 on 2/3/2024 22:22:10 UTC
Most recent: V(122869)/40546771 / 1243743094029841 ‏(‎25656 digits) via code E1 on 4/24/2024 00:10:33 UTC
Entrance Rank: mean 67926.46 (minimum 44282, 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

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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