
theorem
  3847 is prime
proof
  now
    3847 = 2*1923 + 1; hence not 2 divides 3847 by NAT_4:9;
    3847 = 3*1282 + 1; hence not 3 divides 3847 by NAT_4:9;
    3847 = 5*769 + 2; hence not 5 divides 3847 by NAT_4:9;
    3847 = 7*549 + 4; hence not 7 divides 3847 by NAT_4:9;
    3847 = 11*349 + 8; hence not 11 divides 3847 by NAT_4:9;
    3847 = 13*295 + 12; hence not 13 divides 3847 by NAT_4:9;
    3847 = 17*226 + 5; hence not 17 divides 3847 by NAT_4:9;
    3847 = 19*202 + 9; hence not 19 divides 3847 by NAT_4:9;
    3847 = 23*167 + 6; hence not 23 divides 3847 by NAT_4:9;
    3847 = 29*132 + 19; hence not 29 divides 3847 by NAT_4:9;
    3847 = 31*124 + 3; hence not 31 divides 3847 by NAT_4:9;
    3847 = 37*103 + 36; hence not 37 divides 3847 by NAT_4:9;
    3847 = 41*93 + 34; hence not 41 divides 3847 by NAT_4:9;
    3847 = 43*89 + 20; hence not 43 divides 3847 by NAT_4:9;
    3847 = 47*81 + 40; hence not 47 divides 3847 by NAT_4:9;
    3847 = 53*72 + 31; hence not 53 divides 3847 by NAT_4:9;
    3847 = 59*65 + 12; hence not 59 divides 3847 by NAT_4:9;
    3847 = 61*63 + 4; hence not 61 divides 3847 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3847 & n is prime
  holds not n divides 3847 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
