Proth number

plural Proth numbers

1. mathematicsAny number of the form k·2ⁿ + 1, where k is odd, n is a positive integer, and 2ⁿ > k.

   If a Proth number is prime, we call it a Proth prime.

   2014, Adam Spencer, Adam Spencer's Big Book of Numbers, Brio Books, page 388

   2 more examples

   2006, B. Grégoire, L. Théry, B. Werner, A Computational Approach to Pocklington Certificates, Masami Hagiya, Philip Wadler (editors), Functional and Logic Programming: 8th International Symposium, Proceedings, Springer, LNCS 3945, page 109, To generate Pocklington certificates for Proth number we add a new entry to the oracle: pocklington -proth k p.

   Suppose that a Proth number n#61;k2ʳ#43;1 satisfies the condition that a#123;(n-1)#47;2#125;#92;equiv-1#92;pmodn for some integer a. Prove that n is prime.

   2016, Abhijit Das, Computational Number Theory, Taylor & Francis (CRC Press / Chapman & Hall), page 295