
theorem
  1129 is prime
proof
  now
    1129 = 2*564 + 1; hence not 2 divides 1129 by NAT_4:9;
    1129 = 3*376 + 1; hence not 3 divides 1129 by NAT_4:9;
    1129 = 5*225 + 4; hence not 5 divides 1129 by NAT_4:9;
    1129 = 7*161 + 2; hence not 7 divides 1129 by NAT_4:9;
    1129 = 11*102 + 7; hence not 11 divides 1129 by NAT_4:9;
    1129 = 13*86 + 11; hence not 13 divides 1129 by NAT_4:9;
    1129 = 17*66 + 7; hence not 17 divides 1129 by NAT_4:9;
    1129 = 19*59 + 8; hence not 19 divides 1129 by NAT_4:9;
    1129 = 23*49 + 2; hence not 23 divides 1129 by NAT_4:9;
    1129 = 29*38 + 27; hence not 29 divides 1129 by NAT_4:9;
    1129 = 31*36 + 13; hence not 31 divides 1129 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1129 & n is prime
  holds not n divides 1129 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
