# GFact 22 | (2^x + 1 and Prime)

**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 = 2^{n}**. So overall number becomes 2

^{2n}+ 1. Such numbers are called Fermat Number (Numbers of form 2

^{2n}+ 1). The first few Fermet numbers are 3, 5, 17, 257, 65537, 4294967297, ….

An important thing to note is a number of the form 2^{2n} + 1) is not always prime. For example 2^{25} + 1 = 2^{5} + 1 = 2^{32} + 1 = 4294967297 = 641 * 6700417.

This fact is contributed by **Shivam Pradhan (anuj_charm)**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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