
theorem
  967 is prime
proof
  now
    967 = 2*483 + 1; hence not 2 divides 967 by NAT_4:9;
    967 = 3*322 + 1; hence not 3 divides 967 by NAT_4:9;
    967 = 5*193 + 2; hence not 5 divides 967 by NAT_4:9;
    967 = 7*138 + 1; hence not 7 divides 967 by NAT_4:9;
    967 = 11*87 + 10; hence not 11 divides 967 by NAT_4:9;
    967 = 13*74 + 5; hence not 13 divides 967 by NAT_4:9;
    967 = 17*56 + 15; hence not 17 divides 967 by NAT_4:9;
    967 = 19*50 + 17; hence not 19 divides 967 by NAT_4:9;
    967 = 23*42 + 1; hence not 23 divides 967 by NAT_4:9;
    967 = 29*33 + 10; hence not 29 divides 967 by NAT_4:9;
    967 = 31*31 + 6; hence not 31 divides 967 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 967 & n is prime
  holds not n divides 967 by XPRIMET1:22;
  hence thesis by NAT_4:14;
