
theorem
  4481 is prime
proof
  now
    4481 = 2*2240 + 1; hence not 2 divides 4481 by NAT_4:9;
    4481 = 3*1493 + 2; hence not 3 divides 4481 by NAT_4:9;
    4481 = 5*896 + 1; hence not 5 divides 4481 by NAT_4:9;
    4481 = 7*640 + 1; hence not 7 divides 4481 by NAT_4:9;
    4481 = 11*407 + 4; hence not 11 divides 4481 by NAT_4:9;
    4481 = 13*344 + 9; hence not 13 divides 4481 by NAT_4:9;
    4481 = 17*263 + 10; hence not 17 divides 4481 by NAT_4:9;
    4481 = 19*235 + 16; hence not 19 divides 4481 by NAT_4:9;
    4481 = 23*194 + 19; hence not 23 divides 4481 by NAT_4:9;
    4481 = 29*154 + 15; hence not 29 divides 4481 by NAT_4:9;
    4481 = 31*144 + 17; hence not 31 divides 4481 by NAT_4:9;
    4481 = 37*121 + 4; hence not 37 divides 4481 by NAT_4:9;
    4481 = 41*109 + 12; hence not 41 divides 4481 by NAT_4:9;
    4481 = 43*104 + 9; hence not 43 divides 4481 by NAT_4:9;
    4481 = 47*95 + 16; hence not 47 divides 4481 by NAT_4:9;
    4481 = 53*84 + 29; hence not 53 divides 4481 by NAT_4:9;
    4481 = 59*75 + 56; hence not 59 divides 4481 by NAT_4:9;
    4481 = 61*73 + 28; hence not 61 divides 4481 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4481 & n is prime
  holds not n divides 4481 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
