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 02:17:51 CDT)
Database id:5485 (entry last modified on 6/1/2022 04:53:38 CDT)
Program Does *: general
Active primes:on current list: 50, rank by number 15
Total primes: number ever on any list: 62
Production score: for current list 39 (normalized: 0), total 39.1460, rank by score 29
Largest prime: 1050000 + 65859 ‏(‎50001 digits) via code E3 on 6/1/2022 05:06:22 CDT
Most recent: (2117239 + 1)/3 ‏(‎35292 digits) via code E2 on 8/7/2022 13:02:38 CDT
Entrance Rank: mean 70277.68 (minimum 57952, 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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