
theorem
  2393 is prime
proof
  now
    2393 = 2*1196 + 1; hence not 2 divides 2393 by NAT_4:9;
    2393 = 3*797 + 2; hence not 3 divides 2393 by NAT_4:9;
    2393 = 5*478 + 3; hence not 5 divides 2393 by NAT_4:9;
    2393 = 7*341 + 6; hence not 7 divides 2393 by NAT_4:9;
    2393 = 11*217 + 6; hence not 11 divides 2393 by NAT_4:9;
    2393 = 13*184 + 1; hence not 13 divides 2393 by NAT_4:9;
    2393 = 17*140 + 13; hence not 17 divides 2393 by NAT_4:9;
    2393 = 19*125 + 18; hence not 19 divides 2393 by NAT_4:9;
    2393 = 23*104 + 1; hence not 23 divides 2393 by NAT_4:9;
    2393 = 29*82 + 15; hence not 29 divides 2393 by NAT_4:9;
    2393 = 31*77 + 6; hence not 31 divides 2393 by NAT_4:9;
    2393 = 37*64 + 25; hence not 37 divides 2393 by NAT_4:9;
    2393 = 41*58 + 15; hence not 41 divides 2393 by NAT_4:9;
    2393 = 43*55 + 28; hence not 43 divides 2393 by NAT_4:9;
    2393 = 47*50 + 43; hence not 47 divides 2393 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2393 & n is prime
  holds not n divides 2393 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
