
theorem
  3343 is prime
proof
  now
    3343 = 2*1671 + 1; hence not 2 divides 3343 by NAT_4:9;
    3343 = 3*1114 + 1; hence not 3 divides 3343 by NAT_4:9;
    3343 = 5*668 + 3; hence not 5 divides 3343 by NAT_4:9;
    3343 = 7*477 + 4; hence not 7 divides 3343 by NAT_4:9;
    3343 = 11*303 + 10; hence not 11 divides 3343 by NAT_4:9;
    3343 = 13*257 + 2; hence not 13 divides 3343 by NAT_4:9;
    3343 = 17*196 + 11; hence not 17 divides 3343 by NAT_4:9;
    3343 = 19*175 + 18; hence not 19 divides 3343 by NAT_4:9;
    3343 = 23*145 + 8; hence not 23 divides 3343 by NAT_4:9;
    3343 = 29*115 + 8; hence not 29 divides 3343 by NAT_4:9;
    3343 = 31*107 + 26; hence not 31 divides 3343 by NAT_4:9;
    3343 = 37*90 + 13; hence not 37 divides 3343 by NAT_4:9;
    3343 = 41*81 + 22; hence not 41 divides 3343 by NAT_4:9;
    3343 = 43*77 + 32; hence not 43 divides 3343 by NAT_4:9;
    3343 = 47*71 + 6; hence not 47 divides 3343 by NAT_4:9;
    3343 = 53*63 + 4; hence not 53 divides 3343 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3343 & n is prime
  holds not n divides 3343 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
