
theorem
  2503 is prime
proof
  now
    2503 = 2*1251 + 1; hence not 2 divides 2503 by NAT_4:9;
    2503 = 3*834 + 1; hence not 3 divides 2503 by NAT_4:9;
    2503 = 5*500 + 3; hence not 5 divides 2503 by NAT_4:9;
    2503 = 7*357 + 4; hence not 7 divides 2503 by NAT_4:9;
    2503 = 11*227 + 6; hence not 11 divides 2503 by NAT_4:9;
    2503 = 13*192 + 7; hence not 13 divides 2503 by NAT_4:9;
    2503 = 17*147 + 4; hence not 17 divides 2503 by NAT_4:9;
    2503 = 19*131 + 14; hence not 19 divides 2503 by NAT_4:9;
    2503 = 23*108 + 19; hence not 23 divides 2503 by NAT_4:9;
    2503 = 29*86 + 9; hence not 29 divides 2503 by NAT_4:9;
    2503 = 31*80 + 23; hence not 31 divides 2503 by NAT_4:9;
    2503 = 37*67 + 24; hence not 37 divides 2503 by NAT_4:9;
    2503 = 41*61 + 2; hence not 41 divides 2503 by NAT_4:9;
    2503 = 43*58 + 9; hence not 43 divides 2503 by NAT_4:9;
    2503 = 47*53 + 12; hence not 47 divides 2503 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2503 & n is prime
  holds not n divides 2503 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
