
theorem
  3361 is prime
proof
  now
    3361 = 2*1680 + 1; hence not 2 divides 3361 by NAT_4:9;
    3361 = 3*1120 + 1; hence not 3 divides 3361 by NAT_4:9;
    3361 = 5*672 + 1; hence not 5 divides 3361 by NAT_4:9;
    3361 = 7*480 + 1; hence not 7 divides 3361 by NAT_4:9;
    3361 = 11*305 + 6; hence not 11 divides 3361 by NAT_4:9;
    3361 = 13*258 + 7; hence not 13 divides 3361 by NAT_4:9;
    3361 = 17*197 + 12; hence not 17 divides 3361 by NAT_4:9;
    3361 = 19*176 + 17; hence not 19 divides 3361 by NAT_4:9;
    3361 = 23*146 + 3; hence not 23 divides 3361 by NAT_4:9;
    3361 = 29*115 + 26; hence not 29 divides 3361 by NAT_4:9;
    3361 = 31*108 + 13; hence not 31 divides 3361 by NAT_4:9;
    3361 = 37*90 + 31; hence not 37 divides 3361 by NAT_4:9;
    3361 = 41*81 + 40; hence not 41 divides 3361 by NAT_4:9;
    3361 = 43*78 + 7; hence not 43 divides 3361 by NAT_4:9;
    3361 = 47*71 + 24; hence not 47 divides 3361 by NAT_4:9;
    3361 = 53*63 + 22; hence not 53 divides 3361 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3361 & n is prime
  holds not n divides 3361 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
