Most non-negative integers can be written as the sum of a prime number plus a perfect square. For instance, 21 can be written as What is the smallest number greater than 1 which cannot be expressed in this way?

EpicW Oct 1, 2019

#1**+3 **

2 can be written as 2 (a prime) + 0 (a perfect square)

3 can be written as 2 ( a prime) + 1 (a perfect square)

4 can be written as 3 (prime) + 1 (a perfect square)

5 = 5 (a prime) + 0 (a perfect square)

6 = 5 (prime) + 1 (a perfect square)

7 = 3 (prime) + 4 (a perfect square)

8 = 7 (prime) + 1 (perfect square)

9 = 5 (prime) + 4 (perfect square)

10

0 (perfect square) + 10 (non-prime)

1 + 9 sum of two squares

2 (prime) + 8 (non-square)

3 + 7 sum of two primes

4 (perfect square) + 6 (non-prime)

5 + 5 sum of two primes

CPhill Oct 1, 2019