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If I read this properly, you want to know that:

{p | 9p+22 is prime} returns the empty set.

Gut reaction is that this is false, and quick observation shows that it is.

Let p=1

9 * 1 + 22 = 31 and prime. One counterexample is enough to prove falsehood. ■

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Q: Please help in a way a year 9 could understand prove that there is no integer p such that the set p p plus 8 p plus 22 is prime?
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