All numbers can be written as the sum of four squares: n = a^2 + b^2 + c^2 + d^2. Every even number greater than 2 is believed to be the sum of two primes. It is interesting to consider which forms represent all, or almost all, numbers.
Every odd number between 7 and a million can be expressed as the sum of a prime and two even powers of two (that is, p + 2^a + 2^b with p prime and a and b positive). But there are infinitely many odd numbers not of this form! Find the first example.
765 = 253 + 2^9 + 2^1 and 253 is prime, so 765 is not the answer.