
theorem
  1301 is prime
proof
  now
    1301 = 2*650 + 1; hence not 2 divides 1301 by NAT_4:9;
    1301 = 3*433 + 2; hence not 3 divides 1301 by NAT_4:9;
    1301 = 5*260 + 1; hence not 5 divides 1301 by NAT_4:9;
    1301 = 7*185 + 6; hence not 7 divides 1301 by NAT_4:9;
    1301 = 11*118 + 3; hence not 11 divides 1301 by NAT_4:9;
    1301 = 13*100 + 1; hence not 13 divides 1301 by NAT_4:9;
    1301 = 17*76 + 9; hence not 17 divides 1301 by NAT_4:9;
    1301 = 19*68 + 9; hence not 19 divides 1301 by NAT_4:9;
    1301 = 23*56 + 13; hence not 23 divides 1301 by NAT_4:9;
    1301 = 29*44 + 25; hence not 29 divides 1301 by NAT_4:9;
    1301 = 31*41 + 30; hence not 31 divides 1301 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1301 & n is prime
  holds not n divides 1301 by XPRIMET1:22;
  hence thesis by NAT_4:14;
