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

3.6

A number of the form 2x + 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 Fermet 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). 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.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

GATE CS Corner    Company Wise Coding Practice

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.

Recommended Posts:



3.6 Average Difficulty : 3.6/5.0
Based on 6 vote(s)










Writing code in comment? Please use ide.geeksforgeeks.org, generate link and share the link here.