127

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Summary

Factorization

The number 127 is a prime number.

Properties and families

Property or family	Parameter value	First few numbers	Proof of satisfaction/membership/containment
prime number		2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, [SHOW MORE] 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271 View list on OEIS	divide and check
Mersenne number $M_{n}=2^{n}-1$	$n=7$, i.e., $M_{7}=2^{7}-1$		plug and check
Mersenne prime (prime number that is also a Mersenne number)

Prime-generating polynomials

Below are some polynomials that give prime numbers for small input values, which give the value 127 for suitable input choice.

Polynomial	Degree	Some values for which it generates primes	Input value $n$ at which it generates 127
$n^{2}-n+17$	2	all numbers 1-16, because 17 is one of the lucky numbers of Euler.	11
$2n^{2}+29$	2	all numbers 0-28	7