
theorem
  1597 is prime
proof
  now
    1597 = 2*798 + 1; hence not 2 divides 1597 by NAT_4:9;
    1597 = 3*532 + 1; hence not 3 divides 1597 by NAT_4:9;
    1597 = 5*319 + 2; hence not 5 divides 1597 by NAT_4:9;
    1597 = 7*228 + 1; hence not 7 divides 1597 by NAT_4:9;
    1597 = 11*145 + 2; hence not 11 divides 1597 by NAT_4:9;
    1597 = 13*122 + 11; hence not 13 divides 1597 by NAT_4:9;
    1597 = 17*93 + 16; hence not 17 divides 1597 by NAT_4:9;
    1597 = 19*84 + 1; hence not 19 divides 1597 by NAT_4:9;
    1597 = 23*69 + 10; hence not 23 divides 1597 by NAT_4:9;
    1597 = 29*55 + 2; hence not 29 divides 1597 by NAT_4:9;
    1597 = 31*51 + 16; hence not 31 divides 1597 by NAT_4:9;
    1597 = 37*43 + 6; hence not 37 divides 1597 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1597 & n is prime
  holds not n divides 1597 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
