
theorem
  3313 is prime
proof
  now
    3313 = 2*1656 + 1; hence not 2 divides 3313 by NAT_4:9;
    3313 = 3*1104 + 1; hence not 3 divides 3313 by NAT_4:9;
    3313 = 5*662 + 3; hence not 5 divides 3313 by NAT_4:9;
    3313 = 7*473 + 2; hence not 7 divides 3313 by NAT_4:9;
    3313 = 11*301 + 2; hence not 11 divides 3313 by NAT_4:9;
    3313 = 13*254 + 11; hence not 13 divides 3313 by NAT_4:9;
    3313 = 17*194 + 15; hence not 17 divides 3313 by NAT_4:9;
    3313 = 19*174 + 7; hence not 19 divides 3313 by NAT_4:9;
    3313 = 23*144 + 1; hence not 23 divides 3313 by NAT_4:9;
    3313 = 29*114 + 7; hence not 29 divides 3313 by NAT_4:9;
    3313 = 31*106 + 27; hence not 31 divides 3313 by NAT_4:9;
    3313 = 37*89 + 20; hence not 37 divides 3313 by NAT_4:9;
    3313 = 41*80 + 33; hence not 41 divides 3313 by NAT_4:9;
    3313 = 43*77 + 2; hence not 43 divides 3313 by NAT_4:9;
    3313 = 47*70 + 23; hence not 47 divides 3313 by NAT_4:9;
    3313 = 53*62 + 27; hence not 53 divides 3313 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3313 & n is prime
  holds not n divides 3313 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
