Need explanation for hashcode example in Effective Java textbook

Question

Here's the sample code from Item 9:

public final class PhoneNumber {
  private final short areaCode;
  private final short prefix;
  private final short lineNumber;

  @Override
  public int hashCode() {
    int result = 17;
    result = 31 * result + areaCode;
    result = 31 * result + prefix;
    result = 31 * result + lineNumber;
    return result;
  }
}

Pg 48 states: "the value 31 was chosen because it is an odd prime. If it were even and the multiplication overflowed, information would be lost, as muiltiplication by 2 is equivalent to shifting."

I understand the concept of multiplication by 2 being equivalent to bit shifting. I also know that we'll still get an overflow (hence information loss) when we multiply a large number by a large odd prime number. What I don't get is why information loss arising from multiplication by large odd primes is preferable to information loss arising from multiplication by large even numbers.

Answer 1

With an even multiplier the least significant bit, after multiplication, is always zero. With an odd multiplier the least significant bit is either one or zero depending on what the previous value of result was. Hence the even multiplier is losing uncertainty about the low bit, while the odd multiplier is preserving it.