The expression is divisible by 3 if n is odd, and divisible by 5 if n is of the form 4n+2. The net effect is that n must be a multiple of 4. But even then, the expression is divisible by 7, unless the said multiple is also divisible by 3. Hence, if the expression is prime, then 12 divides n.
n=0, n=12, n=36, n=48, are prime solutions.
n=24 is 103×457×61331×20646607.
n=60 is 3144853×3847314239×680874654589×105287080263229

Posted by broll
on 20130506 01:29:17 