
theorem
  8443 is prime
proof
  now
    8443 = 2*4221 + 1; hence not 2 divides 8443 by NAT_4:9;
    8443 = 3*2814 + 1; hence not 3 divides 8443 by NAT_4:9;
    8443 = 5*1688 + 3; hence not 5 divides 8443 by NAT_4:9;
    8443 = 7*1206 + 1; hence not 7 divides 8443 by NAT_4:9;
    8443 = 11*767 + 6; hence not 11 divides 8443 by NAT_4:9;
    8443 = 13*649 + 6; hence not 13 divides 8443 by NAT_4:9;
    8443 = 17*496 + 11; hence not 17 divides 8443 by NAT_4:9;
    8443 = 19*444 + 7; hence not 19 divides 8443 by NAT_4:9;
    8443 = 23*367 + 2; hence not 23 divides 8443 by NAT_4:9;
    8443 = 29*291 + 4; hence not 29 divides 8443 by NAT_4:9;
    8443 = 31*272 + 11; hence not 31 divides 8443 by NAT_4:9;
    8443 = 37*228 + 7; hence not 37 divides 8443 by NAT_4:9;
    8443 = 41*205 + 38; hence not 41 divides 8443 by NAT_4:9;
    8443 = 43*196 + 15; hence not 43 divides 8443 by NAT_4:9;
    8443 = 47*179 + 30; hence not 47 divides 8443 by NAT_4:9;
    8443 = 53*159 + 16; hence not 53 divides 8443 by NAT_4:9;
    8443 = 59*143 + 6; hence not 59 divides 8443 by NAT_4:9;
    8443 = 61*138 + 25; hence not 61 divides 8443 by NAT_4:9;
    8443 = 67*126 + 1; hence not 67 divides 8443 by NAT_4:9;
    8443 = 71*118 + 65; hence not 71 divides 8443 by NAT_4:9;
    8443 = 73*115 + 48; hence not 73 divides 8443 by NAT_4:9;
    8443 = 79*106 + 69; hence not 79 divides 8443 by NAT_4:9;
    8443 = 83*101 + 60; hence not 83 divides 8443 by NAT_4:9;
    8443 = 89*94 + 77; hence not 89 divides 8443 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8443 & n is prime
  holds not n divides 8443 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
