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Reynolds and Brazier's PSieve


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.)

L1115, L1116, L1117, L1118, L1119 ... ... L5158, L5160, L5161, L5162, L5164
E-mail address: (e-mail address unpublished)
Username: PSieve (entry created on 11/22/2009)
Database id:2058 (entry last modified on 10/21/2020)
Program Does *: sieve
Active primes:on current list: 2693, rank by number 3
Total primes: number ever on any list: 20030
Production score: for current list 53 (normalized: 11602), total 53.9708, rank by score 10
Largest prime: 11 · 27971110 - 1 ‏(‎2399545 digits) via code L2484 on 11/25/2019
Most recent: 3457 · 21608760 + 1 ‏(‎484289 digits) via code L5164 on 10/21/2020
Entrance Rank: mean 1358.64 (minimum 24, maximum 49657)

Descriptive Data: (report abuse)

A collection of 'fixed n' sieves capable of quickly processing multiple integer sequences in k and n of the form k*2^n+/-1, where k < 2^62, n < 2^31.

TPSieve: originally developed by Geoff Reynolds for the Twin Prime Search, was meant for use in a sieve with one or a few n's. It was then modified by Ken Brazier, in collaboration with Geoff Reynolds, to make many-n searching efficient, within the fixed-n format. Additional modifications by Ken allowed tpsieve to sieve for the combined forms of k*2^n+1/k*2^n-1.

PPSieve: developed by Ken Brazier, is a modified version of TPSieve that sieves for single primes of the form k*2^n+1. Its strength is the many-n optimization. Also, with the --riesel flag, it can sieve for k*2^n-1.

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