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): No proof-code has created for this entry yet, use the link below to create one.
Active wild codes: ^E\d+
Code prefix:E
E-mail address:
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Username cm (entry created on 5/12/2022 07:17:51 UTC)
Database id:5485 (entry last modified on 6/1/2022 09:53:38 UTC)
Program Does *: general
Active primes:on current list: 62, rank by number 13
Total primes: number ever on any list: 75
Production score: for current list 40 (normalized: 0), total 40.1691, rank by score 29
Largest prime: 5104824 + 1048245 ‏(‎73269 digits) via code E4 on 2/21/2023 18:35:29 UTC
Most recent: (2130439 - 1)/260879 ‏(‎39261 digits) via code E9 on 2/28/2023 22:31:33 UTC
Entrance Rank: mean 68640.00 (minimum 52172, maximum 75522)

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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).
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