37

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Summary

The number 37 is a prime number.

Property or family	Parameter values	First few numbers	Proof of satisfaction/containment/membership
prime number	12th 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
near-square prime of the form $n^{2}+1$	$n=6$ (fourth prime of this form)	2, 5, 17, 37, 101, 197, 257, [SHOW MORE] 401, 577, 677, 1297, 1601, 2917, 3137, 4357, 5477, 7057, 8101, 8837, 12101, 13457, 14401, 15377, 15877, 16901, 17957, 21317, 22501, 24337, 25601, 28901, 30977, 32401, 33857, 41617, 42437, 44101, 50177 View list on OEIS
irregular prime (prime greater than 2 that is not regular)	smallest 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	Fill this in later

Below are some polynomials that give prime numbers for small input values, which give the value 37 for suitable input choice.

Polynomial	Degree	Some values for which it generates primes	Input value $n$ at which it generates 37
$n^{2}-n+17$	2	all numbers 1-16, because 17 is one of the lucky numbers of Euler.	5
$2n^{2}+29$	2	all numbers 0-28	2