Fermat Numbers

Fermat Number, a class of numbers, is an integer of the form $ F_n=2^{2^n} +1 \ \ n \ge 0$ . For example: Putting $ n := 0,1,2 \ldots$ in $ F_n=2^{2^n}$ we get $ F_0=3$ , $ F_1=5$ , $ F_2=17$ , $ F_3=257$ etc. Fermat observed that all the integers $ F_0, F_1, F_2, F_3, \ldots$ were prime numbers and announced that $ F_n$ is a prime for each natural value of $ n$ . In writing to…