The only prime that qualifies is 3.
11+3^2=20=2^2*5
All primes except 2 and 3 can be written as (6n+1) or (6n+5) for positive integer n.
(2 does not qualify. 11+2^2=15=3*5 has only 4 divisors.)
11+(6n+1)^2=36n^2+12n+12=12(n^2+n+1) which has a minimum of 12 divisors if (n^2+n+1) is prime.
11+(6n+5)^2=36n^2+60n+36=12(3n^2+5n+3) which similarly has a minimum of 12 divisors.

Posted by Jer
on 20170515 09:25:46 