
theorem
  3373 is prime
proof
  now
    3373 = 2*1686 + 1; hence not 2 divides 3373 by NAT_4:9;
    3373 = 3*1124 + 1; hence not 3 divides 3373 by NAT_4:9;
    3373 = 5*674 + 3; hence not 5 divides 3373 by NAT_4:9;
    3373 = 7*481 + 6; hence not 7 divides 3373 by NAT_4:9;
    3373 = 11*306 + 7; hence not 11 divides 3373 by NAT_4:9;
    3373 = 13*259 + 6; hence not 13 divides 3373 by NAT_4:9;
    3373 = 17*198 + 7; hence not 17 divides 3373 by NAT_4:9;
    3373 = 19*177 + 10; hence not 19 divides 3373 by NAT_4:9;
    3373 = 23*146 + 15; hence not 23 divides 3373 by NAT_4:9;
    3373 = 29*116 + 9; hence not 29 divides 3373 by NAT_4:9;
    3373 = 31*108 + 25; hence not 31 divides 3373 by NAT_4:9;
    3373 = 37*91 + 6; hence not 37 divides 3373 by NAT_4:9;
    3373 = 41*82 + 11; hence not 41 divides 3373 by NAT_4:9;
    3373 = 43*78 + 19; hence not 43 divides 3373 by NAT_4:9;
    3373 = 47*71 + 36; hence not 47 divides 3373 by NAT_4:9;
    3373 = 53*63 + 34; hence not 53 divides 3373 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3373 & n is prime
  holds not n divides 3373 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
