Yves Gallot's Proth.exe
(Another of the Prime Pages' resources)
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program 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.)

Proof-code(s): SP, DS, MC, L61, p150 ... ... SB10, L446, SB11, L647, p358
Active wild codes: ^g.*,^GF\d+,^GC\d+
Code prefix:g
E-mail address: (e-mail address unpublished)
Web page:http://primes.utm.edu/programs/gallot/index.html
Username: Proth.exe (entry created on 11/30/-1)
Database id:411 (entry last modified on 04/30/2016)
Program Does *: other, special, plus, minus, classical
Active primes:on current list: 120, rank by number 10
Total primes: number ever on any list: 26801
Production score: for current list 51 (normalized: 2370), total 51.5516, rank by score 12
Largest prime: 19249 · 213018586 + 1 ‏(‎3918990 digits) via code SB10 on 05/07/2007
Most recent: 2 · 1225199265 + 1 ‏(‎405813 digits) via code g427 on 06/27/2017
Entrance Rank: mean 418.57 (minimum 4, maximum 6697)

Descriptive Data: (report abuse)
In 1997, the "Proth program" Proth.exe was created by Yves Gallot for the search for large prime factors of Fermat numbers and implemented the following theorem:
Proth's Theorem (1878):
Let N = k*2n + 1 with k < 2n. If there is an integer a such that a(N-1)/2 = -1 (mod N), then N is prime.
Now, the "Proth program" has been expanded to cover the primality test of all numbers N of the form k*bn + 1 or k*bn - 1.

It is designed to allow test of any number of these forms and the largest of them, which can be tested on modern computers, have more than 10,000,000 digits! Then in practice, the difficulty of the test is quickly multiplying the large numbers involved. Proth is highly optimized for the test of large numbers (more than 10,000 digits). Discrete Weighted Transform and Fast Fourier Transform multiplication is used for squaring or multiplying, plus fast modular operations (using the special form of N) are also employed for speed purposes.

Proth.exe has been used to find the most primes (of any program) on the list of Largest Known Primes. It has also been used to find most of the largest known non-Mersenne primes.

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