
theorem
  293 is prime
proof
  now
    293 = 2*146 + 1; hence not 2 divides 293 by NAT_4:9;
    293 = 3*97 + 2; hence not 3 divides 293 by NAT_4:9;
    293 = 5*58 + 3; hence not 5 divides 293 by NAT_4:9;
    293 = 7*41 + 6; hence not 7 divides 293 by NAT_4:9;
    293 = 11*26 + 7; hence not 11 divides 293 by NAT_4:9;
    293 = 13*22 + 7; hence not 13 divides 293 by NAT_4:9;
    293 = 17*17 + 4; hence not 17 divides 293 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 293 & n is prime
  holds not n divides 293 by XPRIMET1:14;
  hence thesis by NAT_4:14;
