Yves Gallot's Cyclo

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):	L4026, p379, L4561, A5, A7, A13, A18, A22
E-mail address:	(e-mail address unpublished)
Web page:	https://github.com/galloty/genefer22/tree/main/cyclo
Username	Cyclo	(entry created on 12/28/2014 22:13:08 UTC)
Database id:	4310	(entry last modified on 3/31/2024 12:38:16 UTC)
Program Does *:	special
Active primes:	on current list: 51, rank by number 18
Total primes:	number ever on any list: 82
Production score:	for current list 54 (normalized: 18749), total 54.9665, rank by score 9
Largest prime:	516693^2097152 - 516693^1048576 + 1 ‏(‎11981518 digits) via code L4561 on 10/2/2023 00:29:30 UTC
Most recent:	669821552¹⁶³⁸⁴ - 669821552⁸¹⁹² + 1 ‏(‎144605 digits) via code A18 on 4/26/2024 09:36:37 UTC
Entrance Rank:	mean 26676.86 (minimum 7, maximum 54300)

Descriptive Data: (report abuse)

Cyclo is a probable primality checker for numbers of the form Φ_3·2ⁿ (b) = Φ₆(b ^{2^n - 1}) = Φ₃(-b ^{2^n - 1}) = b ^2ⁿ - b ^{2^n - 1} + 1.
The test of this form is fast (compared to other programs) due to the use of a discrete transform built with the roots of the polynomial.
It is similar to genefer algorithm (GF_n (b) = Φ_2·2ⁿ (b)): Cyclo is a variant of this program.
The smallest base values yielding these primes are OEIS A246119.

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

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