
theorem
  2441 is prime
proof
  now
    2441 = 2*1220 + 1; hence not 2 divides 2441 by NAT_4:9;
    2441 = 3*813 + 2; hence not 3 divides 2441 by NAT_4:9;
    2441 = 5*488 + 1; hence not 5 divides 2441 by NAT_4:9;
    2441 = 7*348 + 5; hence not 7 divides 2441 by NAT_4:9;
    2441 = 11*221 + 10; hence not 11 divides 2441 by NAT_4:9;
    2441 = 13*187 + 10; hence not 13 divides 2441 by NAT_4:9;
    2441 = 17*143 + 10; hence not 17 divides 2441 by NAT_4:9;
    2441 = 19*128 + 9; hence not 19 divides 2441 by NAT_4:9;
    2441 = 23*106 + 3; hence not 23 divides 2441 by NAT_4:9;
    2441 = 29*84 + 5; hence not 29 divides 2441 by NAT_4:9;
    2441 = 31*78 + 23; hence not 31 divides 2441 by NAT_4:9;
    2441 = 37*65 + 36; hence not 37 divides 2441 by NAT_4:9;
    2441 = 41*59 + 22; hence not 41 divides 2441 by NAT_4:9;
    2441 = 43*56 + 33; hence not 43 divides 2441 by NAT_4:9;
    2441 = 47*51 + 44; hence not 47 divides 2441 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2441 & n is prime
  holds not n divides 2441 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
