
theorem
  2459 is prime
proof
  now
    2459 = 2*1229 + 1; hence not 2 divides 2459 by NAT_4:9;
    2459 = 3*819 + 2; hence not 3 divides 2459 by NAT_4:9;
    2459 = 5*491 + 4; hence not 5 divides 2459 by NAT_4:9;
    2459 = 7*351 + 2; hence not 7 divides 2459 by NAT_4:9;
    2459 = 11*223 + 6; hence not 11 divides 2459 by NAT_4:9;
    2459 = 13*189 + 2; hence not 13 divides 2459 by NAT_4:9;
    2459 = 17*144 + 11; hence not 17 divides 2459 by NAT_4:9;
    2459 = 19*129 + 8; hence not 19 divides 2459 by NAT_4:9;
    2459 = 23*106 + 21; hence not 23 divides 2459 by NAT_4:9;
    2459 = 29*84 + 23; hence not 29 divides 2459 by NAT_4:9;
    2459 = 31*79 + 10; hence not 31 divides 2459 by NAT_4:9;
    2459 = 37*66 + 17; hence not 37 divides 2459 by NAT_4:9;
    2459 = 41*59 + 40; hence not 41 divides 2459 by NAT_4:9;
    2459 = 43*57 + 8; hence not 43 divides 2459 by NAT_4:9;
    2459 = 47*52 + 15; hence not 47 divides 2459 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2459 & n is prime
  holds not n divides 2459 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
