
theorem
  2273 is prime
proof
  now
    2273 = 2*1136 + 1; hence not 2 divides 2273 by NAT_4:9;
    2273 = 3*757 + 2; hence not 3 divides 2273 by NAT_4:9;
    2273 = 5*454 + 3; hence not 5 divides 2273 by NAT_4:9;
    2273 = 7*324 + 5; hence not 7 divides 2273 by NAT_4:9;
    2273 = 11*206 + 7; hence not 11 divides 2273 by NAT_4:9;
    2273 = 13*174 + 11; hence not 13 divides 2273 by NAT_4:9;
    2273 = 17*133 + 12; hence not 17 divides 2273 by NAT_4:9;
    2273 = 19*119 + 12; hence not 19 divides 2273 by NAT_4:9;
    2273 = 23*98 + 19; hence not 23 divides 2273 by NAT_4:9;
    2273 = 29*78 + 11; hence not 29 divides 2273 by NAT_4:9;
    2273 = 31*73 + 10; hence not 31 divides 2273 by NAT_4:9;
    2273 = 37*61 + 16; hence not 37 divides 2273 by NAT_4:9;
    2273 = 41*55 + 18; hence not 41 divides 2273 by NAT_4:9;
    2273 = 43*52 + 37; hence not 43 divides 2273 by NAT_4:9;
    2273 = 47*48 + 17; hence not 47 divides 2273 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2273 & n is prime
  holds not n divides 2273 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
