
theorem
  349 is prime
proof
  now
    349 = 2*174 + 1; hence not 2 divides 349 by NAT_4:9;
    349 = 3*116 + 1; hence not 3 divides 349 by NAT_4:9;
    349 = 5*69 + 4; hence not 5 divides 349 by NAT_4:9;
    349 = 7*49 + 6; hence not 7 divides 349 by NAT_4:9;
    349 = 11*31 + 8; hence not 11 divides 349 by NAT_4:9;
    349 = 13*26 + 11; hence not 13 divides 349 by NAT_4:9;
    349 = 17*20 + 9; hence not 17 divides 349 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 349 & n is prime
  holds not n divides 349 by XPRIMET1:14;
  hence thesis by NAT_4:14;
