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Which word has the highest normalized score according to the following:

• Assign each individual letter A..Z of an (English) word a value corresponding to the n'th prime (see table below).


• Take the product of its letter values.


• Normalization: Take the log10 of that product, and divide by the wordlength.


• (See Python example code below)


• Please state the wordlength along with its score

Examples:

• 
  SYZYGY = 1.83686.. (6 letters)


• 
  WOW = 1.83675.. (3 letters)


• 
  SYZYGIUM = 1.73403.. (8 letters)


• 
  WOODWORKING = 1.56381.. (11 letters)

(The normalization is to prefer everyday English words over IUPAC chemical names or 'Pneumonoultramicroscopicsilicovolcanoconiosis').

Letter values A:2 B:3 C:5 D:7 E:11 F:13 G:17 H:19 I:23 J:29 K:31 L:37 M:41 N:43 O:47 P:53 Q:59 R:61 S:67 T:71 U:73 V:79 W:83 X:89 Y:97 Z:101

Some Python example code:

import string
from math import log10

primes = letter_prime[0]:letter_prime[1] for letter_prime in zip(string.ascii_uppercase, [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101])
'A': 2, 'B': 3, 'C': 5, 'D': 7, 'E': 11, 'F': 13, 'G': 17, 'H': 19, 'I': 23, 'J': 29, 'K': 31, 'L': 37, 'M': 41, 'N': 43, 'O': 47, 'P': 53, 'Q': 59, 'R': 61, 'S': 67, 'T': 71, 'U': 73, 'V': 79, 'W': 83, 'X': 89, 'Y': 97, 'Z': 101

def letter_prime_score(word):
 prod = 1
 for letter in word:
 prod *= primes[letter]
 return log10(prod) / len(word)

letter_prime_score('SYZYGY')
1.8368600501100796

letter_prime_score('WOW')
1.8367513475626218

letter_prime_score('SYZYGIUM')
1.734027889906502

letter_prime_score('WOODWORKING')
1.5638076854903682

The word that I got was ZYZZYVA, a valid Scrabble word, and a type of snouted beetle, most famous for being the final word in the dictionary. The total points are $101^3 times 97^2 times 79 times 2$, which is equal to $1.5316681 times 10^12$. If we normalize this by taking the logarithm and dividing by the number of letters in the word, we get $fraclog 1.5316681 times 10^127 approx 1.74073781098$.

In comparison, SYZYGIUM results in $fraclog 745114679048898 approx 1.73402788991$.

WOODWORKING results in $fraclog 15917854857594760711 approx 1.56380768549$.

PNEUMONOULTRAMICROSCOPICSILICOVOLCANOCONIOSIS results in $fraclog 2.09 times 10^6545 approx 1.45155880636$.

Update
On the other hand, my first suggestion punished long words as much as it favoured small words. Therefore:

1 letter: I results in $fraclog 231 approx 1.36172783602$.

2 letter: XU results in $fraclog 73 times 892 approx 1.90635643338$.
Note: This word found by @Herb Wolfe! Go upvote their answer!! :D

3 letter: ZZZ results in $fraclog 10303013 approx 2.00432137378$.
Note: Check the link for ZZZ, it's in the Merriam Scrabble Dictionary!

4 letter: ZIZZ results in $fraclog 236969234 approx 1.84367298934$.
Note: Apparently ZIZZ is in the Merrriam Scrabble Dictionary too!

5 letter: ZZYZX results in $fraclog 86947101395 approx 1.98785102165$.

6 letter: ZYZZYX results in $fraclog 8627750877016 approx 1.98931626609$.
Note: This word found by @peaceoutside! Go upvote their answer!! :D

7 letter: ZYZZYVA results in $fraclog 1.5316681 times 10^127 approx 1.74073781098$.

8 letter: ZYZZYZUS results in $fraclog 4.7887992 times 10^158 approx 1.96002832831$.

Zyzzyx

is 1.989316266087555

It's a genus of sand wasp, as well as a road, an album title, a film title, a place in California and a few other things.

For two letter words:

Xu, a monetary unit of Viet Nam scores 1.90635...

For three letter words, I came with:

Zuz, an ancient Hebrew silver coin scores 1.95732...

Initially I had thought of

Zax, a tool for cutting roof slates, however it only scores 1.41824...

For a four letter word:

Zizz, to make a buzzing sound. Score: 1.84367

Using the list of words in the souptonuts project and a little Python I get these (word length, score, word) tuples - the first two seem dubious as "English words", but I include them since I'm using that list:

1 2.00432137378 Z
2 2.00432137378 ZZ
3 2.00432137378 ZZZ
4 1.9308059891 TUZZ
5 1.95556308687 WUZZY
6 1.88381542586 XYSTUS
7 1.87044896192 ZYZOMYS
8 1.83260090565 UNTRUSTY
9 1.82296096305 SYSTYLOUS
10 1.84447884826 TOPSYTURVY
11 1.79318782406 TORTUROUSLY
12 1.78637729544 UNTORTUOUSLY
13 1.78210192156 UNTRUSTWORTHY
14 1.77762365381 UNTUMULTUOUSLY
15 1.75526497378 NONTUMULTUOUSLY
16 1.73158108016 UNPRESUMPTUOUSLY
17 1.71182422909 NONTUMULTUOUSNESS
18 1.7002751909 OVERPRESUMPTUOUSLY
19 1.67396629859 OVERSUPERSTITIOUSLY
20 1.6688495362 OVERPRESUMPTUOUSNESS
21 1.64654271243 OVERSUPERSTITIOUSNESS
22 1.5654574758 OTORHINOLARYNGOLOGISTS
23 1.58471955554 PSYCHONEUROIMMUNOLOGIST
24 1.59477602418 PSYCHONEUROIMMUNOLOGISTS
25 1.45302344974 SUPERINCOMPREHENSIBLENESS
26 1.33951040188 ANTIESTABLISHMENTARIANISMS
27 1.53394460557 HYDROXYDESOXYCORTICOSTERONE
28 1.48393646489 HYDROXYDEHYDROCORTICOSTERONE
29 1.532979713 TRINITROPHENYLMETHYLNITRAMINE
30 1.50665471943 HIPPOPOTOMONSTROSESQUIPEDALIAN
31 1.39171062494 DICHLORODIPHENYLTRICHLOROETHANE
32 1.4052845055 DICHLORODIPHENYLTRICHLOROETHANES
34 1.39093530773 DIAMINOPROPYLTETRAMETHYLENEDIAMINE
45 1.45154686507 PNEUMONOULTRAMICROSCOPICSILICOVOLCANOCONIOSIS
58 1.46558961766 LLANFAIRPWLLGWYNGYLLGOGERYCHWYRNDROBWLLLLANTYSILIOGOGOGOCH 

Here is example code in Python 3 (hosted at Try It Online! A site maintained by codegolf.stackexchange moderator Dennis)

• it takes the list of words as input -- that needs changing to access and parse a file with the words in if you want to use it with a huge word list like I did.

So far:

• 4 letters: ZIZZ = 1.84367..


• 6 letters: SYZYGY = 1.83686..


• 3 letters: WOW = 1.83675..


• 5 letters: PROPS = 1.74641..


• 4 letters: ZIPS = 1.7291


• 5 letters: WHUPS = 1.72230..


• 8 letters: PROSPERS = 1.67311..


• 7 letters: PROSPER = 1.65125..


• 6 letters: SPORES = 1.64587..


• 7 letters: ZIPPERS = 1.6382..


• 8 letters: PAROXYSM = 1.60722..

(We added normalization to exclude freaks like PNEUMONOULTRAMICROSCOPICSILICOVOLCANOCONIOSIS which scored a ridiculous 2.09e+65 without normalization, but only 1.45155 after).