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Firstly, I don't understand the point of having both $m$ and $n.$ Since only their product appears, call it $k.$ You are then trying to find the smallest prime congruent to $1$ modulo $k.$ The bound for such is a highly nontrivial matter, see (eg) http://en.wikipedia.org/wiki/Linnik%27s_theorem EDIT It is believed that you don't have to examine more than $\log^2 k$ multiples to find the first prime in a progression of your type. |
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Firstly, I don't understand the point of having both $m$ and $n.$ Since only their product appears, call it $k.$ You are then trying to find the smallest prime congruent to $1$ modulo $k.$ The bound for such is a highly nontrivial matter, see (eg) |
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