Math 2.0

Number theory Definition

Fermat number

Definition

For a natural number nn, the nn-th Fermat number is Fn=22n+1F_n = 2^{2^n} + 1.

Remarks

The first values are F0=3F_0 = 3, F1=5F_1 = 5, F2=17F_2 = 17, F3=257F_3 = 257 and F4=65537F_4 = 65537. The Fermat numbers satisfy F0F1⋯Fn−1=Fn−2F_0 F_1 \cdots F_{n-1} = F_n - 2 for n≥1n \ge 1. A Fermat number that is prime is a Fermat prime.

Where this leads

4 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Fermat_number, lead section
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