
theorem
  653 is prime
proof
  now
    653 = 2*326 + 1; hence not 2 divides 653 by NAT_4:9;
    653 = 3*217 + 2; hence not 3 divides 653 by NAT_4:9;
    653 = 5*130 + 3; hence not 5 divides 653 by NAT_4:9;
    653 = 7*93 + 2; hence not 7 divides 653 by NAT_4:9;
    653 = 11*59 + 4; hence not 11 divides 653 by NAT_4:9;
    653 = 13*50 + 3; hence not 13 divides 653 by NAT_4:9;
    653 = 17*38 + 7; hence not 17 divides 653 by NAT_4:9;
    653 = 19*34 + 7; hence not 19 divides 653 by NAT_4:9;
    653 = 23*28 + 9; hence not 23 divides 653 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 653 & n is prime
  holds not n divides 653 by XPRIMET1:18;
  hence thesis by NAT_4:14;
