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

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## 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 $6 n - 1$:

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

This sequence is A048264 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

## Proof

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## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $161$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $161$