
theorem
  5323 is prime
proof
  now
    5323 = 2*2661 + 1; hence not 2 divides 5323 by NAT_4:9;
    5323 = 3*1774 + 1; hence not 3 divides 5323 by NAT_4:9;
    5323 = 5*1064 + 3; hence not 5 divides 5323 by NAT_4:9;
    5323 = 7*760 + 3; hence not 7 divides 5323 by NAT_4:9;
    5323 = 11*483 + 10; hence not 11 divides 5323 by NAT_4:9;
    5323 = 13*409 + 6; hence not 13 divides 5323 by NAT_4:9;
    5323 = 17*313 + 2; hence not 17 divides 5323 by NAT_4:9;
    5323 = 19*280 + 3; hence not 19 divides 5323 by NAT_4:9;
    5323 = 23*231 + 10; hence not 23 divides 5323 by NAT_4:9;
    5323 = 29*183 + 16; hence not 29 divides 5323 by NAT_4:9;
    5323 = 31*171 + 22; hence not 31 divides 5323 by NAT_4:9;
    5323 = 37*143 + 32; hence not 37 divides 5323 by NAT_4:9;
    5323 = 41*129 + 34; hence not 41 divides 5323 by NAT_4:9;
    5323 = 43*123 + 34; hence not 43 divides 5323 by NAT_4:9;
    5323 = 47*113 + 12; hence not 47 divides 5323 by NAT_4:9;
    5323 = 53*100 + 23; hence not 53 divides 5323 by NAT_4:9;
    5323 = 59*90 + 13; hence not 59 divides 5323 by NAT_4:9;
    5323 = 61*87 + 16; hence not 61 divides 5323 by NAT_4:9;
    5323 = 67*79 + 30; hence not 67 divides 5323 by NAT_4:9;
    5323 = 71*74 + 69; hence not 71 divides 5323 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5323 & n is prime
  holds not n divides 5323 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
