Necessary Limitations
Such a conjecture must be subject to some necessary conditions. For example if we take the two polynomials x + 4 and x + 7, there is no n > 0 for which n + 4 and n + 7 are both primes. That is because one will be an even number > 2, and the other an odd number. The main question in formulating the conjecture is to rule out this phenomenon.
Read more about this topic: Schinzel's Hypothesis H
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