
theorem
  1499 is prime
proof
  now
    1499 = 2*749 + 1; hence not 2 divides 1499 by NAT_4:9;
    1499 = 3*499 + 2; hence not 3 divides 1499 by NAT_4:9;
    1499 = 5*299 + 4; hence not 5 divides 1499 by NAT_4:9;
    1499 = 7*214 + 1; hence not 7 divides 1499 by NAT_4:9;
    1499 = 11*136 + 3; hence not 11 divides 1499 by NAT_4:9;
    1499 = 13*115 + 4; hence not 13 divides 1499 by NAT_4:9;
    1499 = 17*88 + 3; hence not 17 divides 1499 by NAT_4:9;
    1499 = 19*78 + 17; hence not 19 divides 1499 by NAT_4:9;
    1499 = 23*65 + 4; hence not 23 divides 1499 by NAT_4:9;
    1499 = 29*51 + 20; hence not 29 divides 1499 by NAT_4:9;
    1499 = 31*48 + 11; hence not 31 divides 1499 by NAT_4:9;
    1499 = 37*40 + 19; hence not 37 divides 1499 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1499 & n is prime
  holds not n divides 1499 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
