59

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Summary

Factorization

The number 59 is a prime number.

Properties and families

Property or family	Parameter values	First few numbers	Proof of satisfaction/membership/containment
prime number	17th 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
irregular prime	second irregular prime	37, 59, 67, 101, 103, 131, 149, 157, 233, 257, 263, [SHOW MORE] 271, 283, 293, 307, 311, 347, 353, 379, 389, 401, 409, 421, 433, 461, 463, 467, 491, 523, 541, 547, 557, 577, 587, 593, 607, 613, 617, 619, 631, 647, 653, 659, 673, 677, 683, 691, 727, 751, 757, 761, 773, 797, 809, 811, 821, 827, 839, 877, 881, 887, 929, 953, 971, 1061 View list on OEIS
safe prime (prime $p$ such that $(p-1)/2$ is also prime)	fifth safe prime	5, 7, 11, 23, 47, 59, 83, 107, 167, [SHOW MORE] 179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459, 2579, 2819, 2879, 2903 View list on OEIS	$(59-1)/2$ equals 29 which is prime.
smaller of a pair of twin primes			59 + 2 = 61 which is prime.

Prime-generating polynomials

Below are some polynomials that give prime numbers for small input values, which give the value 59 for suitable input choice.

Polynomial	Degree	Some values for which it generates primes	Input value $n$ at which it generates 59
$n^{2}-n+17$	2	all numbers 1-16, because 17 is one of the lucky numbers of Euler.	7