2015Acta ArithmeticaOpen access

Primality test for numbers of the form (2p)2n+1

Yingpu Deng, Dandan Huang

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Abstract

We describe a primality test for $M=(2p)^{2^n}+1$ with an odd prime $p$ and a positive integer $n$, which are a particular type of generalized Fermat numbers. We also present special primality criteria for all odd prime numbers $p$ not exceeding $19$. All

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We describe a primality test for $M=(2p)^{2^n}+1$ with an odd prime $p$ and a positive integer $n$, which are a particular type of generalized Fermat numbers. We also present special primality criteria for all odd prime numbers $p$ not exceeding $19$. All

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Available abstract

We describe a primality test for $M=(2p)^{2^n}+1$ with an odd prime $p$ and a positive integer $n$, which are a particular type of generalized Fermat numbers. We also present special primality criteria for all odd prime numbers $p$ not exceeding $19$. All

Key concepts: Primality test, Mathematics, Fermat's Last Theorem, Prime (order theory), Integer (computer science), Combinatorics, Discrete mathematics, Arithmetic

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