
theorem
  2909 is prime
proof
  now
    2909 = 2*1454 + 1; hence not 2 divides 2909 by NAT_4:9;
    2909 = 3*969 + 2; hence not 3 divides 2909 by NAT_4:9;
    2909 = 5*581 + 4; hence not 5 divides 2909 by NAT_4:9;
    2909 = 7*415 + 4; hence not 7 divides 2909 by NAT_4:9;
    2909 = 11*264 + 5; hence not 11 divides 2909 by NAT_4:9;
    2909 = 13*223 + 10; hence not 13 divides 2909 by NAT_4:9;
    2909 = 17*171 + 2; hence not 17 divides 2909 by NAT_4:9;
    2909 = 19*153 + 2; hence not 19 divides 2909 by NAT_4:9;
    2909 = 23*126 + 11; hence not 23 divides 2909 by NAT_4:9;
    2909 = 29*100 + 9; hence not 29 divides 2909 by NAT_4:9;
    2909 = 31*93 + 26; hence not 31 divides 2909 by NAT_4:9;
    2909 = 37*78 + 23; hence not 37 divides 2909 by NAT_4:9;
    2909 = 41*70 + 39; hence not 41 divides 2909 by NAT_4:9;
    2909 = 43*67 + 28; hence not 43 divides 2909 by NAT_4:9;
    2909 = 47*61 + 42; hence not 47 divides 2909 by NAT_4:9;
    2909 = 53*54 + 47; hence not 53 divides 2909 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2909 & n is prime
  holds not n divides 2909 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
