
theorem
  809 is prime
proof
  now
    809 = 2*404 + 1; hence not 2 divides 809 by NAT_4:9;
    809 = 3*269 + 2; hence not 3 divides 809 by NAT_4:9;
    809 = 5*161 + 4; hence not 5 divides 809 by NAT_4:9;
    809 = 7*115 + 4; hence not 7 divides 809 by NAT_4:9;
    809 = 11*73 + 6; hence not 11 divides 809 by NAT_4:9;
    809 = 13*62 + 3; hence not 13 divides 809 by NAT_4:9;
    809 = 17*47 + 10; hence not 17 divides 809 by NAT_4:9;
    809 = 19*42 + 11; hence not 19 divides 809 by NAT_4:9;
    809 = 23*35 + 4; hence not 23 divides 809 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 809 & n is prime
  holds not n divides 809 by XPRIMET1:18;
  hence thesis by NAT_4:14;
