
theorem
  3853 is prime
proof
  now
    3853 = 2*1926 + 1; hence not 2 divides 3853 by NAT_4:9;
    3853 = 3*1284 + 1; hence not 3 divides 3853 by NAT_4:9;
    3853 = 5*770 + 3; hence not 5 divides 3853 by NAT_4:9;
    3853 = 7*550 + 3; hence not 7 divides 3853 by NAT_4:9;
    3853 = 11*350 + 3; hence not 11 divides 3853 by NAT_4:9;
    3853 = 13*296 + 5; hence not 13 divides 3853 by NAT_4:9;
    3853 = 17*226 + 11; hence not 17 divides 3853 by NAT_4:9;
    3853 = 19*202 + 15; hence not 19 divides 3853 by NAT_4:9;
    3853 = 23*167 + 12; hence not 23 divides 3853 by NAT_4:9;
    3853 = 29*132 + 25; hence not 29 divides 3853 by NAT_4:9;
    3853 = 31*124 + 9; hence not 31 divides 3853 by NAT_4:9;
    3853 = 37*104 + 5; hence not 37 divides 3853 by NAT_4:9;
    3853 = 41*93 + 40; hence not 41 divides 3853 by NAT_4:9;
    3853 = 43*89 + 26; hence not 43 divides 3853 by NAT_4:9;
    3853 = 47*81 + 46; hence not 47 divides 3853 by NAT_4:9;
    3853 = 53*72 + 37; hence not 53 divides 3853 by NAT_4:9;
    3853 = 59*65 + 18; hence not 59 divides 3853 by NAT_4:9;
    3853 = 61*63 + 10; hence not 61 divides 3853 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3853 & n is prime
  holds not n divides 3853 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
