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As Jim Lyon explains:
Any prime number other than 2 has to be odd, and therefore can be expressed as 2*k+1, where k is an integer.
Take the difference between k2 and (k+1)2,
using simple algebra, (k+1)2 - k2 = 2*k+1.
So not only is the prime other than two expressed as a difference of two squares, but it is a difference ot the squares of two specific consecutive numbers.
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