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it is provable that: if you take all the prime numbers up to n raised to any power, split them into two groups, multiply, and subtract the smaller product from the larger; if the result is less than (n+1)^2, then its prime.

what's the likelyhood of the result being prime when its between (n+1)^2 and 2*(n+1)^2?

(to put it another way, how many composite numbers are between (n+1)^2 and 2*(n+1)^2 and not evenly divisible by any number less than n?)

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