
theorem
  2447 is prime
proof
  now
    2447 = 2*1223 + 1; hence not 2 divides 2447 by NAT_4:9;
    2447 = 3*815 + 2; hence not 3 divides 2447 by NAT_4:9;
    2447 = 5*489 + 2; hence not 5 divides 2447 by NAT_4:9;
    2447 = 7*349 + 4; hence not 7 divides 2447 by NAT_4:9;
    2447 = 11*222 + 5; hence not 11 divides 2447 by NAT_4:9;
    2447 = 13*188 + 3; hence not 13 divides 2447 by NAT_4:9;
    2447 = 17*143 + 16; hence not 17 divides 2447 by NAT_4:9;
    2447 = 19*128 + 15; hence not 19 divides 2447 by NAT_4:9;
    2447 = 23*106 + 9; hence not 23 divides 2447 by NAT_4:9;
    2447 = 29*84 + 11; hence not 29 divides 2447 by NAT_4:9;
    2447 = 31*78 + 29; hence not 31 divides 2447 by NAT_4:9;
    2447 = 37*66 + 5; hence not 37 divides 2447 by NAT_4:9;
    2447 = 41*59 + 28; hence not 41 divides 2447 by NAT_4:9;
    2447 = 43*56 + 39; hence not 43 divides 2447 by NAT_4:9;
    2447 = 47*52 + 3; hence not 47 divides 2447 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2447 & n is prime
  holds not n divides 2447 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
