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]
Legendre's conjecture, also one of Landau's open prime
problems from 1912 and still unproven, states that there is
at least ONE prime number between two consecutive square
numbers n^2 and (n+1)^2. n=36=6^2 is the first square where
the number N of the primes between 36^2 and 37^2 is a
square number itself, i.e., N=3^2: primes 1297, 1301, 1303,
1307, 1319, 1321, 1327, 1361, 1367. [Zschorn]
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