
theorem
  811 is prime
proof
  now
    811 = 2*405 + 1; hence not 2 divides 811 by NAT_4:9;
    811 = 3*270 + 1; hence not 3 divides 811 by NAT_4:9;
    811 = 5*162 + 1; hence not 5 divides 811 by NAT_4:9;
    811 = 7*115 + 6; hence not 7 divides 811 by NAT_4:9;
    811 = 11*73 + 8; hence not 11 divides 811 by NAT_4:9;
    811 = 13*62 + 5; hence not 13 divides 811 by NAT_4:9;
    811 = 17*47 + 12; hence not 17 divides 811 by NAT_4:9;
    811 = 19*42 + 13; hence not 19 divides 811 by NAT_4:9;
    811 = 23*35 + 6; hence not 23 divides 811 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 811 & n is prime
  holds not n divides 811 by XPRIMET1:18;
  hence thesis by NAT_4:14;
