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primenumbers@yahoogroups.com, "pbtoau" <PbtoAu@...> wrote:

>

> I have been looking at the factorizations of the number at the middle of prime gaps. I notice that for the gap 210, that 2 is always a factor but never 3, 5 or 7. What is the mathematical explanation for this? I assume that the middle of a gap of 2310 would never have the factors 3, 5, 7 or 11.

If the smaller prime is p1, the middle integer is m=p1+210/2=p1+105

Since p1 is odd, m is even.

Since 105 is divisible by 3, 5 and 7, and p1 isn't, m can't be.

Sim. for your 2310 case, mutatis mutandis.

Mike