M is the smallest possible sum for a set of four distinct primes such that the sum of any three is prime - (p1,p2,p3,p4}.
N is the smallest possible sum for a set of six distinct primes such that the sum of any five is prime - (q1,q2,q3,q4,q5,q6}.

Find M & N and the corresponding sets.

An even easier proof that 5 is impossible.  Pick any four numbers in the set that do not include 2.  There is always at least one such set. They are all odd and sum to a non-prime even number.

Posted by Steve Herman on 2019-02-05 19:30:05