
theorem
  3469 is prime
proof
  now
    3469 = 2*1734 + 1; hence not 2 divides 3469 by NAT_4:9;
    3469 = 3*1156 + 1; hence not 3 divides 3469 by NAT_4:9;
    3469 = 5*693 + 4; hence not 5 divides 3469 by NAT_4:9;
    3469 = 7*495 + 4; hence not 7 divides 3469 by NAT_4:9;
    3469 = 11*315 + 4; hence not 11 divides 3469 by NAT_4:9;
    3469 = 13*266 + 11; hence not 13 divides 3469 by NAT_4:9;
    3469 = 17*204 + 1; hence not 17 divides 3469 by NAT_4:9;
    3469 = 19*182 + 11; hence not 19 divides 3469 by NAT_4:9;
    3469 = 23*150 + 19; hence not 23 divides 3469 by NAT_4:9;
    3469 = 29*119 + 18; hence not 29 divides 3469 by NAT_4:9;
    3469 = 31*111 + 28; hence not 31 divides 3469 by NAT_4:9;
    3469 = 37*93 + 28; hence not 37 divides 3469 by NAT_4:9;
    3469 = 41*84 + 25; hence not 41 divides 3469 by NAT_4:9;
    3469 = 43*80 + 29; hence not 43 divides 3469 by NAT_4:9;
    3469 = 47*73 + 38; hence not 47 divides 3469 by NAT_4:9;
    3469 = 53*65 + 24; hence not 53 divides 3469 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3469 & n is prime
  holds not n divides 3469 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
