Prime Internet Eisenstein Search
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
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project 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 reflect on the primes currently on the list. (Many of the terms that are used here are explained on another page.)
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Proof-code(s):
p72, f1, f2, f3, f4 ... ... L4026, p379, L4142, L4506, L4561
E-mail address: (e-mail address unpublished)
Web page:http://fatphil.org/maths/PIES/
Username: PIES (entry created on 09/05/2003)
Database id:541 (entry last modified on 02/22/2017)
Active primes:on current list: 90, rank by number 5
Total primes: number ever on any list: 1425
Production score: for current list 52 (normalized: 6576), total 52.5513, rank by score 4
Largest prime: Phi(3, - 123447524288) ‏(‎5338805 digits) via code L4561 on 02/23/2017
Most recent: Phi(3, - 169312732768) ‏(‎408204 digits) via code p379 on 11/01/2017
Entrance Rank: mean 1408.10 (minimum 12, maximum 4138)

Descriptive Data: (report abuse)
A search for Generalised Eisenstein Fermat numbers, numbers of form Phi(2^s*3^t,b). These are to the Eisenstein integers Z(ω) what Generalised Fermat Numbers are to the Rational and Gaussian Integers.

Featuring an entirely new sieve, and an entirely new proving algorithm. See the project web-page for more details.

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