65537 (number)

← 65536 65537 65538 →
List of numbers — Integers ← 0 10k 20k 30k 40k 50k 60k 70k 80k 90k →
Cardinal	sixty-five thousand five hundred thirty-seven
Ordinal	65537th (sixty-five thousand five hundred and thirty-seventh)
Factorization	65537
Prime	Yes
Roman numeral	LXVDXXXVII
Binary	100000000000000012
Ternary	100222200223
Quaternary	1000000014
Quinary	40441225
Senary	12232256
Octal	2000018
Duodecimal	31B1512
Hexadecimal	1000116
Vigesimal	83GH20
Base 36	1EKH36

65537 is the integer after 65536 and before 65538.

65537 is the largest known prime number of the form ${\displaystyle 2^{2^{n}}+1}$ (${\displaystyle n=4}$). Therefore, a regular polygon with 65537 sides is constructible with compass and unmarked straightedge. In number theory, primes of this form are known as Fermat primes, named after the mathematician Pierre de Fermat. The only known prime Fermat numbers are

${\displaystyle 2^{2^{0}}+1=2^{1}+1=3,}$

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