#!/usr/bin/env python3
def isprime(n):
 return n>1 and all(n%d for d in range(2,int(n**.5)+1))
for seed in ([1,2,3,4,5,7],[1,2,3,5,7,8,6],[1,2,3,5,7,8,12],[1,2,3,5,7,8,4]):
 A=set(seed);step=0
 while True:
  P={a+b for a in A for b in A if a+b<=113 and isprime(a+b)}-A
  if not P:break
  A|=P;step+=1;print(seed,'round',step,sorted(P),flush=True)
 print(seed,'closure',len(A),'113 in sum?',113 in {a+b for a in A for b in A},'witness',[(a,113-a) for a in sorted(A) if a<113-a and 113-a in A])