
theorem
  3463 is prime
proof
  now
    3463 = 2*1731 + 1; hence not 2 divides 3463 by NAT_4:9;
    3463 = 3*1154 + 1; hence not 3 divides 3463 by NAT_4:9;
    3463 = 5*692 + 3; hence not 5 divides 3463 by NAT_4:9;
    3463 = 7*494 + 5; hence not 7 divides 3463 by NAT_4:9;
    3463 = 11*314 + 9; hence not 11 divides 3463 by NAT_4:9;
    3463 = 13*266 + 5; hence not 13 divides 3463 by NAT_4:9;
    3463 = 17*203 + 12; hence not 17 divides 3463 by NAT_4:9;
    3463 = 19*182 + 5; hence not 19 divides 3463 by NAT_4:9;
    3463 = 23*150 + 13; hence not 23 divides 3463 by NAT_4:9;
    3463 = 29*119 + 12; hence not 29 divides 3463 by NAT_4:9;
    3463 = 31*111 + 22; hence not 31 divides 3463 by NAT_4:9;
    3463 = 37*93 + 22; hence not 37 divides 3463 by NAT_4:9;
    3463 = 41*84 + 19; hence not 41 divides 3463 by NAT_4:9;
    3463 = 43*80 + 23; hence not 43 divides 3463 by NAT_4:9;
    3463 = 47*73 + 32; hence not 47 divides 3463 by NAT_4:9;
    3463 = 53*65 + 18; hence not 53 divides 3463 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3463 & n is prime
  holds not n divides 3463 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
