
theorem
  1181 is prime
proof
  now
    1181 = 2*590 + 1; hence not 2 divides 1181 by NAT_4:9;
    1181 = 3*393 + 2; hence not 3 divides 1181 by NAT_4:9;
    1181 = 5*236 + 1; hence not 5 divides 1181 by NAT_4:9;
    1181 = 7*168 + 5; hence not 7 divides 1181 by NAT_4:9;
    1181 = 11*107 + 4; hence not 11 divides 1181 by NAT_4:9;
    1181 = 13*90 + 11; hence not 13 divides 1181 by NAT_4:9;
    1181 = 17*69 + 8; hence not 17 divides 1181 by NAT_4:9;
    1181 = 19*62 + 3; hence not 19 divides 1181 by NAT_4:9;
    1181 = 23*51 + 8; hence not 23 divides 1181 by NAT_4:9;
    1181 = 29*40 + 21; hence not 29 divides 1181 by NAT_4:9;
    1181 = 31*38 + 3; hence not 31 divides 1181 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1181 & n is prime
  holds not n divides 1181 by XPRIMET1:22;
  hence thesis by NAT_4:14;
