# 45

This number is a composite.

Every number greater than 45 is (probably) the sum of distinct primes greater than or equal to eleven. [Gupta]

If the first five positive powers of two are each subtracted from 45 all results are prime. [Trotter]

The common alphabetical value of the three primes 41, 59 and 61 in Roman numerals-based representation. Note that XLI, LIX and LXI are the only valid permutations of the numerals L, X and I. [Necula]

The only known multidigit number n (up to 10^9) such that, n = reversal(sigma(n) - phi(n)) = reversal(sigma(n)) - reversal(phi(n)). [Capelle]

4^5 + 45 is prime. [Homewood]

German mathematician Ernst Kummer set about calculating cubic Gauss sums — after plowing through 45 sums, corresponding to the first 45 non-trivial prime numbers, he finally gave up. [Sloman]

The product of first 45 odd numbers minus 2, i.e., 1*3*5*7*…*89-2, is the largest prime less than a googol of this form. [Loungrides]

(45, 54) is the only pair of double-digit composite numbers (ab, ba) such that ab * ba + 1 is a 2-sphenic number, i.e., 45 * 54 + 1 = 2431 = 11 x 13 x 17. [Loungrides]

The sum of the first (4+5) three-digit primes' digit-products equals 45 which is the sum of one to (4+5). [Worrom]