Solvers will naturally begin by identifying all the famous people shown here.

This should be duck soup; most of these should be familiar, and image search should help to resolve any that they don’t know.

Solvers should next observe that the number of digits in the large number labeling an image (including the ?) matches the length of that person’s full name. They can then extract the letter from the name in the position corresponding to the ? in the digit sequence (people are listed in row-major order):

So solvers get the message ROLL A PASSPHRASE. What does this mean? This is a clue that the puzzle uses Diceware, a system for generating passphrases by rolling dice. For each desired word/component of your passphrase, you roll five ordinary d6 dice, obtaining a five-digit number, and then look up this number in a provided list of 6⁵ = 7776 unique words. This puzzle uses the original Diceware word list; also see the Diceware Passphrase home page for more detailed information.

Once they find the Diceware word list, solvers should observe that all the famous names are in fact constructable out of words on this list (thanks to the inclusion of many names and name-y bits). The word “factors” in the flavortext, plus the use of the capital Greek letter Π in the title/flavortext suggest that multiplication may be involved (in mathematics, Π is used to denote a product, just as capital Σ denotes a sum). If you break the names into their Diceware-word pieces and then multiply all the associated five-digit numbers, you in fact get the very numbers that label each image, but with the ?s replaced by actual digits:

Solvers now need to figure out what to do with this string of digits: 123334417258758.

It certainly looks like it could be the numeric label for another Diceware-word decomposed name, and in fact it is.

Solvers need to factor this number (“factor” is in the flavortext) to obtain: 2 × 3³ × 19 × 1193 × 2917 × 34543.

Now, 34543 is the Diceware number that maps to JOHN, which is very promising. But aren’t there multiple ways to multiply the other factors to get pairs of numbers? Yes, but there’s only one way to get three five-digit numbers whose digits all in the range 1-6, as required by Diceware (see the appendix).

This unique factorization is 34543 × 55423 × 64422 (listing the factors in ascending order), leading to JOHN × STALL × WORTH. So the puzzle’s answer is JOHN STALLWORTH.

import re

rolls = [i for i in range(11111, 66667) 
         if re.match('^[1-6]*$', str(i))]

def dicefactor(l, i, n):
   if n == 1:
       print(' x '.join([str(x) for x in l]))
   else:
       for j in range(i, len(rolls)):
           rj = rolls[j]
           if n % rj == 0:
               dicefactor(l + [rj], j, n // rj)

dicefactor([], 0, 123334417258758)