As Proth primes have simple binary representations, they have also been used in fast modular reduction without the need for pre-computation, for example by Microsoft.

Dec 22, 2025 · This provides an easy computational test for Proth primes. Yves Gallot has written a downloadable program for testing Proth primes and many of the largest currently known …

Though actually not a true class of primes, the primes of the form k. 2 n +1 with 2 n > k are often called the Proth primes. They are named after the self taught farmer François Proth who lived …

Definition A Proth number is a natural number of the form: N = k ×2n + 1 N = k × 2 n + 1 where: k k is an odd integer n n is a positive integer 2n> k 2 n> k The condition is included, otherwise …

It is still an open question whether an infinite number of Proth primes exist. It was shown in 2022 that the reciprocal sum of Proth primes converges to a real number near 0.747392479, …

As Proth primes have simple binary representations, they have also been used in fast modular reduction without the need for pre-computation, for example by Microsoft.

In number theory, Proth's theorem is a theorem which forms the basis of a primality test for Proth numbers known as Proth's test. Proth numbers, sometimes called Proth Numbers of the First …

In number theory, a Proth number is a number of the form N = k •2 n +1 where k is an odd positive integer and n is a positive integer such that 2 n > k. Without the condition that 2 n > k, …

As Proth primes have simple binary representations, they have also been used in fast modular reduction without the need for pre-computation, for example by Microsoft.

Feb 9, 2018 · Thanks to this theorem, Yves Gallot created an algorithm used in a primality-testing program employed by the Seventeen or Bust project. The first few Proth primes are 3, 5, 13, …