# Even Integers not Sum of 2 Twin Primes

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## Theorem

The following even integers cannot be expressed as the sum of $2$ prime numbers which are each one of a pair of twin primes:

- $2, 4, 94, 96, 98, 400, 402, 404, \ldots$

This sequence is A007534 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

This article is complete as far as it goes, but it could do with expansion.In particular: add a page to the effect that it is conjectured that this list is complete.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Expand}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Proof

This theorem requires a proof.In particular: Can be demonstrated by brute force. A pseudocode program and a printout may be adequate, but first we need to develop a standard language-agnostic $\mathsf{Pr} \infty \mathsf{fWiki}$ pseudocode.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{ProofWanted}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $94$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $94$