Fermat number

A kind of number

About Fermat number

A Fermat number has the form F_n = 2^(2^n) + 1. Only five Fermat numbers are known to be prime: F_0 = 3, F_1 = 5, F_2 = 17, F_3 = 257, F_4 = 65537. Larger F_n are composite or unknown.

Key features

  • Named after Pierre de Fermat; he conjectured all were prime.
  • F_5 through F_32 and many larger are known to be composite.

Examples:

3, 5, 17, 257, 65537

Further reading