# Integers not Expressible as Sum of Distinct Primes of form 6n-1

## Theorem

$161$ is the largest integer that cannot be expressed as the sum of distinct primes of the form $6 n - 1$.

The following integers cannot be expressed as the sum of distinct primes of the form $6 n - 1$:

$1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 18, 19, 20, 21, 24, 25, 26, 27, 30, 31, 32, 35, 36, 37, 38, 42, 43, 44, 48, 49, 50,$
$54, 55, 60, 61, 65, 66, 67, 72, 73, 77, 78, 79, 84, 90, 91, 95, 96, 102, 108, 114, 119, 120, 125, 143, 155, 161$