
theorem
  4463 is prime
proof
  now
    4463 = 2*2231 + 1; hence not 2 divides 4463 by NAT_4:9;
    4463 = 3*1487 + 2; hence not 3 divides 4463 by NAT_4:9;
    4463 = 5*892 + 3; hence not 5 divides 4463 by NAT_4:9;
    4463 = 7*637 + 4; hence not 7 divides 4463 by NAT_4:9;
    4463 = 11*405 + 8; hence not 11 divides 4463 by NAT_4:9;
    4463 = 13*343 + 4; hence not 13 divides 4463 by NAT_4:9;
    4463 = 17*262 + 9; hence not 17 divides 4463 by NAT_4:9;
    4463 = 19*234 + 17; hence not 19 divides 4463 by NAT_4:9;
    4463 = 23*194 + 1; hence not 23 divides 4463 by NAT_4:9;
    4463 = 29*153 + 26; hence not 29 divides 4463 by NAT_4:9;
    4463 = 31*143 + 30; hence not 31 divides 4463 by NAT_4:9;
    4463 = 37*120 + 23; hence not 37 divides 4463 by NAT_4:9;
    4463 = 41*108 + 35; hence not 41 divides 4463 by NAT_4:9;
    4463 = 43*103 + 34; hence not 43 divides 4463 by NAT_4:9;
    4463 = 47*94 + 45; hence not 47 divides 4463 by NAT_4:9;
    4463 = 53*84 + 11; hence not 53 divides 4463 by NAT_4:9;
    4463 = 59*75 + 38; hence not 59 divides 4463 by NAT_4:9;
    4463 = 61*73 + 10; hence not 61 divides 4463 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4463 & n is prime
  holds not n divides 4463 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
