
theorem
  3889 is prime
proof
  now
    3889 = 2*1944 + 1; hence not 2 divides 3889 by NAT_4:9;
    3889 = 3*1296 + 1; hence not 3 divides 3889 by NAT_4:9;
    3889 = 5*777 + 4; hence not 5 divides 3889 by NAT_4:9;
    3889 = 7*555 + 4; hence not 7 divides 3889 by NAT_4:9;
    3889 = 11*353 + 6; hence not 11 divides 3889 by NAT_4:9;
    3889 = 13*299 + 2; hence not 13 divides 3889 by NAT_4:9;
    3889 = 17*228 + 13; hence not 17 divides 3889 by NAT_4:9;
    3889 = 19*204 + 13; hence not 19 divides 3889 by NAT_4:9;
    3889 = 23*169 + 2; hence not 23 divides 3889 by NAT_4:9;
    3889 = 29*134 + 3; hence not 29 divides 3889 by NAT_4:9;
    3889 = 31*125 + 14; hence not 31 divides 3889 by NAT_4:9;
    3889 = 37*105 + 4; hence not 37 divides 3889 by NAT_4:9;
    3889 = 41*94 + 35; hence not 41 divides 3889 by NAT_4:9;
    3889 = 43*90 + 19; hence not 43 divides 3889 by NAT_4:9;
    3889 = 47*82 + 35; hence not 47 divides 3889 by NAT_4:9;
    3889 = 53*73 + 20; hence not 53 divides 3889 by NAT_4:9;
    3889 = 59*65 + 54; hence not 59 divides 3889 by NAT_4:9;
    3889 = 61*63 + 46; hence not 61 divides 3889 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3889 & n is prime
  holds not n divides 3889 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
