
theorem
  3391 is prime
proof
  now
    3391 = 2*1695 + 1; hence not 2 divides 3391 by NAT_4:9;
    3391 = 3*1130 + 1; hence not 3 divides 3391 by NAT_4:9;
    3391 = 5*678 + 1; hence not 5 divides 3391 by NAT_4:9;
    3391 = 7*484 + 3; hence not 7 divides 3391 by NAT_4:9;
    3391 = 11*308 + 3; hence not 11 divides 3391 by NAT_4:9;
    3391 = 13*260 + 11; hence not 13 divides 3391 by NAT_4:9;
    3391 = 17*199 + 8; hence not 17 divides 3391 by NAT_4:9;
    3391 = 19*178 + 9; hence not 19 divides 3391 by NAT_4:9;
    3391 = 23*147 + 10; hence not 23 divides 3391 by NAT_4:9;
    3391 = 29*116 + 27; hence not 29 divides 3391 by NAT_4:9;
    3391 = 31*109 + 12; hence not 31 divides 3391 by NAT_4:9;
    3391 = 37*91 + 24; hence not 37 divides 3391 by NAT_4:9;
    3391 = 41*82 + 29; hence not 41 divides 3391 by NAT_4:9;
    3391 = 43*78 + 37; hence not 43 divides 3391 by NAT_4:9;
    3391 = 47*72 + 7; hence not 47 divides 3391 by NAT_4:9;
    3391 = 53*63 + 52; hence not 53 divides 3391 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3391 & n is prime
  holds not n divides 3391 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
