The document discusses finding the sum of all positive prime numbers x such that x + 2x^2 is also prime. It determines that the only number satisfying these conditions is x = 3, and provides the working to explain why no other values of x are possible.

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Solution
What is the sum of all positive prime numbers such that is also a prime?x + 2x2
Clearly, satisfies the conditions. If then, since is prime, it is not divisible by . So either or for some .
In both cases, is divisible by and is greater than , so it is not a prime.
x = 3 x ≠ 3 x 3 x = 3k + 1 x = 3k + 2 k
+ 2x2
3 3
A Prime Quadratic
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