
theorem
  1163 is prime
proof
  now
    1163 = 2*581 + 1; hence not 2 divides 1163 by NAT_4:9;
    1163 = 3*387 + 2; hence not 3 divides 1163 by NAT_4:9;
    1163 = 5*232 + 3; hence not 5 divides 1163 by NAT_4:9;
    1163 = 7*166 + 1; hence not 7 divides 1163 by NAT_4:9;
    1163 = 11*105 + 8; hence not 11 divides 1163 by NAT_4:9;
    1163 = 13*89 + 6; hence not 13 divides 1163 by NAT_4:9;
    1163 = 17*68 + 7; hence not 17 divides 1163 by NAT_4:9;
    1163 = 19*61 + 4; hence not 19 divides 1163 by NAT_4:9;
    1163 = 23*50 + 13; hence not 23 divides 1163 by NAT_4:9;
    1163 = 29*40 + 3; hence not 29 divides 1163 by NAT_4:9;
    1163 = 31*37 + 16; hence not 31 divides 1163 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1163 & n is prime
  holds not n divides 1163 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
