
theorem
  733 is prime
proof
  now
    733 = 2*366 + 1; hence not 2 divides 733 by NAT_4:9;
    733 = 3*244 + 1; hence not 3 divides 733 by NAT_4:9;
    733 = 5*146 + 3; hence not 5 divides 733 by NAT_4:9;
    733 = 7*104 + 5; hence not 7 divides 733 by NAT_4:9;
    733 = 11*66 + 7; hence not 11 divides 733 by NAT_4:9;
    733 = 13*56 + 5; hence not 13 divides 733 by NAT_4:9;
    733 = 17*43 + 2; hence not 17 divides 733 by NAT_4:9;
    733 = 19*38 + 11; hence not 19 divides 733 by NAT_4:9;
    733 = 23*31 + 20; hence not 23 divides 733 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 733 & n is prime
  holds not n divides 733 by XPRIMET1:18;
  hence thesis by NAT_4:14;
