
theorem
  1811 is prime
proof
  now
    1811 = 2*905 + 1; hence not 2 divides 1811 by NAT_4:9;
    1811 = 3*603 + 2; hence not 3 divides 1811 by NAT_4:9;
    1811 = 5*362 + 1; hence not 5 divides 1811 by NAT_4:9;
    1811 = 7*258 + 5; hence not 7 divides 1811 by NAT_4:9;
    1811 = 11*164 + 7; hence not 11 divides 1811 by NAT_4:9;
    1811 = 13*139 + 4; hence not 13 divides 1811 by NAT_4:9;
    1811 = 17*106 + 9; hence not 17 divides 1811 by NAT_4:9;
    1811 = 19*95 + 6; hence not 19 divides 1811 by NAT_4:9;
    1811 = 23*78 + 17; hence not 23 divides 1811 by NAT_4:9;
    1811 = 29*62 + 13; hence not 29 divides 1811 by NAT_4:9;
    1811 = 31*58 + 13; hence not 31 divides 1811 by NAT_4:9;
    1811 = 37*48 + 35; hence not 37 divides 1811 by NAT_4:9;
    1811 = 41*44 + 7; hence not 41 divides 1811 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1811 & n is prime
  holds not n divides 1811 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
