
theorem
  3823 is prime
proof
  now
    3823 = 2*1911 + 1; hence not 2 divides 3823 by NAT_4:9;
    3823 = 3*1274 + 1; hence not 3 divides 3823 by NAT_4:9;
    3823 = 5*764 + 3; hence not 5 divides 3823 by NAT_4:9;
    3823 = 7*546 + 1; hence not 7 divides 3823 by NAT_4:9;
    3823 = 11*347 + 6; hence not 11 divides 3823 by NAT_4:9;
    3823 = 13*294 + 1; hence not 13 divides 3823 by NAT_4:9;
    3823 = 17*224 + 15; hence not 17 divides 3823 by NAT_4:9;
    3823 = 19*201 + 4; hence not 19 divides 3823 by NAT_4:9;
    3823 = 23*166 + 5; hence not 23 divides 3823 by NAT_4:9;
    3823 = 29*131 + 24; hence not 29 divides 3823 by NAT_4:9;
    3823 = 31*123 + 10; hence not 31 divides 3823 by NAT_4:9;
    3823 = 37*103 + 12; hence not 37 divides 3823 by NAT_4:9;
    3823 = 41*93 + 10; hence not 41 divides 3823 by NAT_4:9;
    3823 = 43*88 + 39; hence not 43 divides 3823 by NAT_4:9;
    3823 = 47*81 + 16; hence not 47 divides 3823 by NAT_4:9;
    3823 = 53*72 + 7; hence not 53 divides 3823 by NAT_4:9;
    3823 = 59*64 + 47; hence not 59 divides 3823 by NAT_4:9;
    3823 = 61*62 + 41; hence not 61 divides 3823 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3823 & n is prime
  holds not n divides 3823 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
