Math 2.0

Number theory Definition

Fermat prime

Builds on Fermat numberPrime number

Definition

A Fermat prime is a Fermat number Fn=22n+1F_n = 2^{2^n} + 1 that is a prime number.

Remarks

The numbers F0,…,F4F_0, \dots, F_4, that is 3,5,17,257,655373, 5, 17, 257, 65537, are prime. No other Fermat prime is known. Fermat conjectured that all Fermat numbers are prime. Euler refuted this in 1732 with F5=641⋅6700417F_5 = 641 \cdot 6700417. A regular nn-gon is constructible with ruler and compass if and only if nn is a power of 22 times distinct Fermat primes. This is the Gauss–Wantzel theorem.

Reading path

To understand this page from the ground up, read these 4 pages in order. The foundations come first.

Show the path as a graph
Divisibility, definition, no evidence levelDivisibilitydefinitionFermat number, definition, no evidence levelFermat numberdefinitionPrime number, definition, no evidence levelPrime numberdefinitionFermat prime, definition, no evidence levelFermat primedefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Divisibility definition
  2. Fermat number definition
  3. Prime number definition
  4. Fermat prime definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Fermat_number, Primality
About this page
Tag0N9E4G2P97
URIm2://0N9E4G2P97
Kinddefinition
WritingW1 stated
MSC11A41
DefinesFermat prime
UsesFermat number, Prime number

Markdown · JSON · Edit on GitHub

What this page needs for W2

  • edge instance_of in: one example (0 of 1)
  • edge not_instance_of in: one non-example that fails one clause (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

No page links to this page yet.