
theorem
  2269 is prime
proof
  now
    2269 = 2*1134 + 1; hence not 2 divides 2269 by NAT_4:9;
    2269 = 3*756 + 1; hence not 3 divides 2269 by NAT_4:9;
    2269 = 5*453 + 4; hence not 5 divides 2269 by NAT_4:9;
    2269 = 7*324 + 1; hence not 7 divides 2269 by NAT_4:9;
    2269 = 11*206 + 3; hence not 11 divides 2269 by NAT_4:9;
    2269 = 13*174 + 7; hence not 13 divides 2269 by NAT_4:9;
    2269 = 17*133 + 8; hence not 17 divides 2269 by NAT_4:9;
    2269 = 19*119 + 8; hence not 19 divides 2269 by NAT_4:9;
    2269 = 23*98 + 15; hence not 23 divides 2269 by NAT_4:9;
    2269 = 29*78 + 7; hence not 29 divides 2269 by NAT_4:9;
    2269 = 31*73 + 6; hence not 31 divides 2269 by NAT_4:9;
    2269 = 37*61 + 12; hence not 37 divides 2269 by NAT_4:9;
    2269 = 41*55 + 14; hence not 41 divides 2269 by NAT_4:9;
    2269 = 43*52 + 33; hence not 43 divides 2269 by NAT_4:9;
    2269 = 47*48 + 13; hence not 47 divides 2269 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2269 & n is prime
  holds not n divides 2269 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
