# Non-Square Positive Integers not Sum of Square and Prime/Examples/10

$10$ cannot be expressed as the sum of a square and a prime.
Testing each $m \in \Z_{>0}$ such that $m^2 < 10$ it is established that there is no solution to $10 - m^2 = p$ where $p$ is prime:
 $\displaystyle 10 - 1^2$ $=$ $\displaystyle 9$ which is composite: $9 = 3^2$ $\displaystyle 10 - 2^2$ $=$ $\displaystyle 6$ which is composite: $6 = 2 \times 3$ $\displaystyle 10 - 3^2$ $=$ $\displaystyle 1$ $1$ is not Prime
$\blacksquare$