
theorem
  5503 is prime
proof
  now
    5503 = 2*2751 + 1; hence not 2 divides 5503 by NAT_4:9;
    5503 = 3*1834 + 1; hence not 3 divides 5503 by NAT_4:9;
    5503 = 5*1100 + 3; hence not 5 divides 5503 by NAT_4:9;
    5503 = 7*786 + 1; hence not 7 divides 5503 by NAT_4:9;
    5503 = 11*500 + 3; hence not 11 divides 5503 by NAT_4:9;
    5503 = 13*423 + 4; hence not 13 divides 5503 by NAT_4:9;
    5503 = 17*323 + 12; hence not 17 divides 5503 by NAT_4:9;
    5503 = 19*289 + 12; hence not 19 divides 5503 by NAT_4:9;
    5503 = 23*239 + 6; hence not 23 divides 5503 by NAT_4:9;
    5503 = 29*189 + 22; hence not 29 divides 5503 by NAT_4:9;
    5503 = 31*177 + 16; hence not 31 divides 5503 by NAT_4:9;
    5503 = 37*148 + 27; hence not 37 divides 5503 by NAT_4:9;
    5503 = 41*134 + 9; hence not 41 divides 5503 by NAT_4:9;
    5503 = 43*127 + 42; hence not 43 divides 5503 by NAT_4:9;
    5503 = 47*117 + 4; hence not 47 divides 5503 by NAT_4:9;
    5503 = 53*103 + 44; hence not 53 divides 5503 by NAT_4:9;
    5503 = 59*93 + 16; hence not 59 divides 5503 by NAT_4:9;
    5503 = 61*90 + 13; hence not 61 divides 5503 by NAT_4:9;
    5503 = 67*82 + 9; hence not 67 divides 5503 by NAT_4:9;
    5503 = 71*77 + 36; hence not 71 divides 5503 by NAT_4:9;
    5503 = 73*75 + 28; hence not 73 divides 5503 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5503 & n is prime
  holds not n divides 5503 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
