# 36

This number is a composite.

The word 'PRIMETEST' is prime when written in radix 36 using 'A'=10, 'B'=11, ... 'Z'=36. In decimal this number is 72684117341741. [Caldwell]

The exact number of ways to partition the integer 36 is prime.

The smallest number which is the sum of two distinct odd primes in four ways (36 = 5 + 31 = 7 + 29 = 13 + 23 = 17 + 19). [McCranie]

The smallest square that is the sum of a Twin prime pair {17, 19}. [Trotter]

The smallest number expressible as the sum of consecutive primes in two ways (5 + 7 + 11 + 13 and 17 + 19). [De Geest]

The smallest multi-digit number such that both 36*63+1 and 36*63-1 are prime. [Gupta]

The smallest triangular number whose sum of divisors as well as sum of aliquot divisors is also a triangular number. [Gupta]

The smallest power (greater than 1) which is not a prime power. [Gupta]

The smallest even number that cannot be expressed in any of these forms: 2n, 2np, with p an odd prime, p+1 with p an odd prime (e.g., 36 = 2232, 36 = 35 + 1, but 35 is not prime). [Rodrigo]

The smallest square n such that if you square the n first prime numbers and add them up, the result is a prime number. [Capelle]

5+7+11+13 is the smallest square number expressible as the sum of four consecutive primes which are also two couples of prime twins! [Herault]

(There is one curio for this number that has not yet been approved by an editor.)