
theorem
  3467 is prime
proof
  now
    3467 = 2*1733 + 1; hence not 2 divides 3467 by NAT_4:9;
    3467 = 3*1155 + 2; hence not 3 divides 3467 by NAT_4:9;
    3467 = 5*693 + 2; hence not 5 divides 3467 by NAT_4:9;
    3467 = 7*495 + 2; hence not 7 divides 3467 by NAT_4:9;
    3467 = 11*315 + 2; hence not 11 divides 3467 by NAT_4:9;
    3467 = 13*266 + 9; hence not 13 divides 3467 by NAT_4:9;
    3467 = 17*203 + 16; hence not 17 divides 3467 by NAT_4:9;
    3467 = 19*182 + 9; hence not 19 divides 3467 by NAT_4:9;
    3467 = 23*150 + 17; hence not 23 divides 3467 by NAT_4:9;
    3467 = 29*119 + 16; hence not 29 divides 3467 by NAT_4:9;
    3467 = 31*111 + 26; hence not 31 divides 3467 by NAT_4:9;
    3467 = 37*93 + 26; hence not 37 divides 3467 by NAT_4:9;
    3467 = 41*84 + 23; hence not 41 divides 3467 by NAT_4:9;
    3467 = 43*80 + 27; hence not 43 divides 3467 by NAT_4:9;
    3467 = 47*73 + 36; hence not 47 divides 3467 by NAT_4:9;
    3467 = 53*65 + 22; hence not 53 divides 3467 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3467 & n is prime
  holds not n divides 3467 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
