
theorem
  1171 is prime
proof
  now
    1171 = 2*585 + 1; hence not 2 divides 1171 by NAT_4:9;
    1171 = 3*390 + 1; hence not 3 divides 1171 by NAT_4:9;
    1171 = 5*234 + 1; hence not 5 divides 1171 by NAT_4:9;
    1171 = 7*167 + 2; hence not 7 divides 1171 by NAT_4:9;
    1171 = 11*106 + 5; hence not 11 divides 1171 by NAT_4:9;
    1171 = 13*90 + 1; hence not 13 divides 1171 by NAT_4:9;
    1171 = 17*68 + 15; hence not 17 divides 1171 by NAT_4:9;
    1171 = 19*61 + 12; hence not 19 divides 1171 by NAT_4:9;
    1171 = 23*50 + 21; hence not 23 divides 1171 by NAT_4:9;
    1171 = 29*40 + 11; hence not 29 divides 1171 by NAT_4:9;
    1171 = 31*37 + 24; hence not 31 divides 1171 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1171 & n is prime
  holds not n divides 1171 by XPRIMET1:22;
  hence thesis by NAT_4:14;
