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Do you think that the formula p = 6n + 1 where n is a whole number, will produce a prime number more than 50% of the time?

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    6(1) + 1 = 7
    6(2) + 1 = 13
    6(3) + 1 = 19
    6(4) + 1 = 25
    6(5) + 1 = 31
    6(6) + 1 = 37
    6(7) + 1 = 43
    6(8) + 1 = 49

    Clearly no.

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