good hash table primes
In the course of designing a good hashing configuration^{}, it is helpful to have a list of prime numbers for the hash table size.
The following is such a list. It has the properties that:

1.
each number in the list is prime

2.
each number is slightly less than twice the size of the previous

3.
each number is as far as possible from the nearest two powers of two
Using primes for hash tables is a good idea because it minimizes clustering in the hashed table. Item (2) is nice because it is convenient for growing a hash table in the face of expanding data. Item (3) has, allegedly, been shown to yield especially good results in practice.
And here is the list:
lwr  upr  % err  prime 

${2}^{5}$  ${2}^{6}$  10.416667  53 
${2}^{6}$  ${2}^{7}$  1.041667  97 
${2}^{7}$  ${2}^{8}$  0.520833  193 
${2}^{8}$  ${2}^{9}$  1.302083  389 
${2}^{9}$  ${2}^{10}$  0.130208  769 
${2}^{10}$  ${2}^{11}$  0.455729  1543 
${2}^{11}$  ${2}^{12}$  0.227865  3079 
${2}^{12}$  ${2}^{13}$  0.113932  6151 
${2}^{13}$  ${2}^{14}$  0.008138  12289 
${2}^{14}$  ${2}^{15}$  0.069173  24593 
${2}^{15}$  ${2}^{16}$  0.010173  49157 
${2}^{16}$  ${2}^{17}$  0.013224  98317 
${2}^{17}$  ${2}^{18}$  0.002543  196613 
${2}^{18}$  ${2}^{19}$  0.006358  393241 
${2}^{19}$  ${2}^{20}$  0.000127  786433 
${2}^{20}$  ${2}^{21}$  0.000318  1572869 
${2}^{21}$  ${2}^{22}$  0.000350  3145739 
${2}^{22}$  ${2}^{23}$  0.000207  6291469 
${2}^{23}$  ${2}^{24}$  0.000040  12582917 
${2}^{24}$  ${2}^{25}$  0.000075  25165843 
${2}^{25}$  ${2}^{26}$  0.000010  50331653 
${2}^{26}$  ${2}^{27}$  0.000023  100663319 
${2}^{27}$  ${2}^{28}$  0.000009  201326611 
${2}^{28}$  ${2}^{29}$  0.000001  402653189 
${2}^{29}$  ${2}^{30}$  0.000011  805306457 
${2}^{30}$  ${2}^{31}$  0.000000  1610612741 
The columns are, in order, the lower bounding power of two, the upper bounding power of two, the relative deviation (in percent) of the prime number^{} from the optimal middle of the first two, and finally the prime itself.
Happy hashing!
Title  good hash table primes 

Canonical name  GoodHashTablePrimes 
Date of creation  20130322 12:57:37 
Last modified on  20130322 12:57:37 
Owner  akrowne (2) 
Last modified by  akrowne (2) 
Numerical id  10 
Author  akrowne (2) 
Entry type  Result 
Classification  msc 68P05 
Classification  msc 68P10 
Classification  msc 68P20 