
theorem
  1823 is prime
proof
  now
    1823 = 2*911 + 1; hence not 2 divides 1823 by NAT_4:9;
    1823 = 3*607 + 2; hence not 3 divides 1823 by NAT_4:9;
    1823 = 5*364 + 3; hence not 5 divides 1823 by NAT_4:9;
    1823 = 7*260 + 3; hence not 7 divides 1823 by NAT_4:9;
    1823 = 11*165 + 8; hence not 11 divides 1823 by NAT_4:9;
    1823 = 13*140 + 3; hence not 13 divides 1823 by NAT_4:9;
    1823 = 17*107 + 4; hence not 17 divides 1823 by NAT_4:9;
    1823 = 19*95 + 18; hence not 19 divides 1823 by NAT_4:9;
    1823 = 23*79 + 6; hence not 23 divides 1823 by NAT_4:9;
    1823 = 29*62 + 25; hence not 29 divides 1823 by NAT_4:9;
    1823 = 31*58 + 25; hence not 31 divides 1823 by NAT_4:9;
    1823 = 37*49 + 10; hence not 37 divides 1823 by NAT_4:9;
    1823 = 41*44 + 19; hence not 41 divides 1823 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1823 & n is prime
  holds not n divides 1823 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
