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Sieve of Eratosthenes

GFact | 2x + 1(where x > 0) is prime if and only if x is a power of 2

Last Updated : 17 Oct, 2023

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A number of the form 2^x + 1 (where x > 0) is prime if and only if x is a power of 2, i.e., x = 2ⁿ. So overall number becomes 2²ⁿ + 1. Such numbers are called Fermat Number (Numbers of form 2²ⁿ + 1). The first few Fermat numbers are 3, 5, 17, 257, 65537, 4294967297, .... An important thing to note is a number of the form 2²ⁿ + 1) is not always prime. For example 2²⁵ + 1 = 2⁵ + 1 = 2³² + 1 = 4294967297 = 641 * 6700417. This fact is contributed by Shivam Pradhan (anuj_charm).

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