
theorem
  3499 is prime
proof
  now
    3499 = 2*1749 + 1; hence not 2 divides 3499 by NAT_4:9;
    3499 = 3*1166 + 1; hence not 3 divides 3499 by NAT_4:9;
    3499 = 5*699 + 4; hence not 5 divides 3499 by NAT_4:9;
    3499 = 7*499 + 6; hence not 7 divides 3499 by NAT_4:9;
    3499 = 11*318 + 1; hence not 11 divides 3499 by NAT_4:9;
    3499 = 13*269 + 2; hence not 13 divides 3499 by NAT_4:9;
    3499 = 17*205 + 14; hence not 17 divides 3499 by NAT_4:9;
    3499 = 19*184 + 3; hence not 19 divides 3499 by NAT_4:9;
    3499 = 23*152 + 3; hence not 23 divides 3499 by NAT_4:9;
    3499 = 29*120 + 19; hence not 29 divides 3499 by NAT_4:9;
    3499 = 31*112 + 27; hence not 31 divides 3499 by NAT_4:9;
    3499 = 37*94 + 21; hence not 37 divides 3499 by NAT_4:9;
    3499 = 41*85 + 14; hence not 41 divides 3499 by NAT_4:9;
    3499 = 43*81 + 16; hence not 43 divides 3499 by NAT_4:9;
    3499 = 47*74 + 21; hence not 47 divides 3499 by NAT_4:9;
    3499 = 53*66 + 1; hence not 53 divides 3499 by NAT_4:9;
    3499 = 59*59 + 18; hence not 59 divides 3499 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3499 & n is prime
  holds not n divides 3499 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
