
theorem
  1097 is prime
proof
  now
    1097 = 2*548 + 1; hence not 2 divides 1097 by NAT_4:9;
    1097 = 3*365 + 2; hence not 3 divides 1097 by NAT_4:9;
    1097 = 5*219 + 2; hence not 5 divides 1097 by NAT_4:9;
    1097 = 7*156 + 5; hence not 7 divides 1097 by NAT_4:9;
    1097 = 11*99 + 8; hence not 11 divides 1097 by NAT_4:9;
    1097 = 13*84 + 5; hence not 13 divides 1097 by NAT_4:9;
    1097 = 17*64 + 9; hence not 17 divides 1097 by NAT_4:9;
    1097 = 19*57 + 14; hence not 19 divides 1097 by NAT_4:9;
    1097 = 23*47 + 16; hence not 23 divides 1097 by NAT_4:9;
    1097 = 29*37 + 24; hence not 29 divides 1097 by NAT_4:9;
    1097 = 31*35 + 12; hence not 31 divides 1097 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1097 & n is prime
  holds not n divides 1097 by XPRIMET1:22;
  hence thesis by NAT_4:14;
