Let n be any odd number

We can represent an odd number n to be = 2p+1 where p is any integer. Since n lies between 7 and 15 inclusive , p= 3, 4, 5, 6, 7.

If p=3, n= 3+3+1 or 3+2+2, which is a sum of three prime numbers

p=4, n= 4+4+1 or 3+3+3 --------------------

p=5, n=5+5+1 or 3+3+5 ---------------------

p=6, n=6+6+1 or 3+5+5 ---------------------

p=7, n=7+7+1 or 3+5+7 --------------------

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