Why is the size 127 (prime) better than 128 for a hash-table?

Question

Supposing simple uniform hashing, that being, any given value is equally like to hash into any of the slots of the hash. Why is it better to use a table of size 127 and not 128?

Answer 1

here is a way to understand " k % 127 depends on all bits of k. k % 128 only depends on the 7 lowest bits." .
k % 128 is equals to k & (2^7-1) .for example: 129 % 128 = 1 , In Binary: 1000 0001 & 0111 1111 =0000 0001,any hight bit of (2^7-1) will be 0 ,which means it dose not matter whats the high position is. but this translate is invalid for numbers which are not equals 2^n.
now let's take a look at how we do division in Decimal 129 % 127 ,first look at the highest position 1,less than 127,then we get the next item 2 combine with fist we get 12 , 12 is less than 127,then combine with 9 which means 129 ,divided by 127 the remainder is 2,we could write this in math:129 = 1 * 127 +2 ,so we got 2 [all of this is called Long_division] ,and it's the same in Binary division,now ,we know k % 127 depends on all bits of k