
theorem
  2239 is prime
proof
  now
    2239 = 2*1119 + 1; hence not 2 divides 2239 by NAT_4:9;
    2239 = 3*746 + 1; hence not 3 divides 2239 by NAT_4:9;
    2239 = 5*447 + 4; hence not 5 divides 2239 by NAT_4:9;
    2239 = 7*319 + 6; hence not 7 divides 2239 by NAT_4:9;
    2239 = 11*203 + 6; hence not 11 divides 2239 by NAT_4:9;
    2239 = 13*172 + 3; hence not 13 divides 2239 by NAT_4:9;
    2239 = 17*131 + 12; hence not 17 divides 2239 by NAT_4:9;
    2239 = 19*117 + 16; hence not 19 divides 2239 by NAT_4:9;
    2239 = 23*97 + 8; hence not 23 divides 2239 by NAT_4:9;
    2239 = 29*77 + 6; hence not 29 divides 2239 by NAT_4:9;
    2239 = 31*72 + 7; hence not 31 divides 2239 by NAT_4:9;
    2239 = 37*60 + 19; hence not 37 divides 2239 by NAT_4:9;
    2239 = 41*54 + 25; hence not 41 divides 2239 by NAT_4:9;
    2239 = 43*52 + 3; hence not 43 divides 2239 by NAT_4:9;
    2239 = 47*47 + 30; hence not 47 divides 2239 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2239 & n is prime
  holds not n divides 2239 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
