**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.

Since we are getting to proofs (which I applaud): my (simplistic) proof, that I indeed found the minimal M and N, is that I searched further, adding together any and all primes just beyond the "minimal" M and N sums that I found, and these yielded no lesser M and N's. Since any newly considered prime will add beyond M and N, I indeed found the two minima. QED

*Edited on ***February 6, 2019, 3:02 am**