
theorem
  2411 is prime
proof
  now
    2411 = 2*1205 + 1; hence not 2 divides 2411 by NAT_4:9;
    2411 = 3*803 + 2; hence not 3 divides 2411 by NAT_4:9;
    2411 = 5*482 + 1; hence not 5 divides 2411 by NAT_4:9;
    2411 = 7*344 + 3; hence not 7 divides 2411 by NAT_4:9;
    2411 = 11*219 + 2; hence not 11 divides 2411 by NAT_4:9;
    2411 = 13*185 + 6; hence not 13 divides 2411 by NAT_4:9;
    2411 = 17*141 + 14; hence not 17 divides 2411 by NAT_4:9;
    2411 = 19*126 + 17; hence not 19 divides 2411 by NAT_4:9;
    2411 = 23*104 + 19; hence not 23 divides 2411 by NAT_4:9;
    2411 = 29*83 + 4; hence not 29 divides 2411 by NAT_4:9;
    2411 = 31*77 + 24; hence not 31 divides 2411 by NAT_4:9;
    2411 = 37*65 + 6; hence not 37 divides 2411 by NAT_4:9;
    2411 = 41*58 + 33; hence not 41 divides 2411 by NAT_4:9;
    2411 = 43*56 + 3; hence not 43 divides 2411 by NAT_4:9;
    2411 = 47*51 + 14; hence not 47 divides 2411 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2411 & n is prime
  holds not n divides 2411 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
