
theorem
  1117 is prime
proof
  now
    1117 = 2*558 + 1; hence not 2 divides 1117 by NAT_4:9;
    1117 = 3*372 + 1; hence not 3 divides 1117 by NAT_4:9;
    1117 = 5*223 + 2; hence not 5 divides 1117 by NAT_4:9;
    1117 = 7*159 + 4; hence not 7 divides 1117 by NAT_4:9;
    1117 = 11*101 + 6; hence not 11 divides 1117 by NAT_4:9;
    1117 = 13*85 + 12; hence not 13 divides 1117 by NAT_4:9;
    1117 = 17*65 + 12; hence not 17 divides 1117 by NAT_4:9;
    1117 = 19*58 + 15; hence not 19 divides 1117 by NAT_4:9;
    1117 = 23*48 + 13; hence not 23 divides 1117 by NAT_4:9;
    1117 = 29*38 + 15; hence not 29 divides 1117 by NAT_4:9;
    1117 = 31*36 + 1; hence not 31 divides 1117 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1117 & n is prime
  holds not n divides 1117 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
