
theorem
  5003 is prime
proof
  now
    5003 = 2*2501 + 1; hence not 2 divides 5003 by NAT_4:9;
    5003 = 3*1667 + 2; hence not 3 divides 5003 by NAT_4:9;
    5003 = 5*1000 + 3; hence not 5 divides 5003 by NAT_4:9;
    5003 = 7*714 + 5; hence not 7 divides 5003 by NAT_4:9;
    5003 = 11*454 + 9; hence not 11 divides 5003 by NAT_4:9;
    5003 = 13*384 + 11; hence not 13 divides 5003 by NAT_4:9;
    5003 = 17*294 + 5; hence not 17 divides 5003 by NAT_4:9;
    5003 = 19*263 + 6; hence not 19 divides 5003 by NAT_4:9;
    5003 = 23*217 + 12; hence not 23 divides 5003 by NAT_4:9;
    5003 = 29*172 + 15; hence not 29 divides 5003 by NAT_4:9;
    5003 = 31*161 + 12; hence not 31 divides 5003 by NAT_4:9;
    5003 = 37*135 + 8; hence not 37 divides 5003 by NAT_4:9;
    5003 = 41*122 + 1; hence not 41 divides 5003 by NAT_4:9;
    5003 = 43*116 + 15; hence not 43 divides 5003 by NAT_4:9;
    5003 = 47*106 + 21; hence not 47 divides 5003 by NAT_4:9;
    5003 = 53*94 + 21; hence not 53 divides 5003 by NAT_4:9;
    5003 = 59*84 + 47; hence not 59 divides 5003 by NAT_4:9;
    5003 = 61*82 + 1; hence not 61 divides 5003 by NAT_4:9;
    5003 = 67*74 + 45; hence not 67 divides 5003 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5003 & n is prime
  holds not n divides 5003 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
