Perhaps the most famous starship number in Sci-Fi, did Gene Roddenberry choose this number at random, or, as with all good art is it a part of a repeating (if hidden) motif?
Replace letters with numbers from 1(A) to 26(Z)
(or to save time just type them into Gematrinator http://www.gematrinator.com/calculator/index.php
If we add the numbers up "James T Kirk" = 117
Oddly enough, "Jean Luc Picard" also sums to 117
Its unlikely but fair to argue that this is just chance - but perhaps consider the name was devised to carry over the same numeric relationship.
Both captains ship registrations are 1701 as every fan of the show knows - its on screen often enough - OK not the exact same number as 117 but composed of the same, also the 0 is not used in the name calculations since we always begin at 1 so it may be fair to disregard 0.
Again is this random chance, just seeing patterns like a numerical pareidolia, or, is there something special (at least to the creator of the show) about this number combination?
This may extend outside of Trek, several, perhaps as many as 3 people reading this will be bouncing up and down in their seats just dying to point out that 117 is also the number of Halo's Master Chief, John-117, arguably the most famous scifi videogame character of the modern era - perhaps a hidden nod toward Kirk and the Enterprise? Are there any others?
Maybe it is coincidence (at the very least its interesting trivia for trekkies) but the practice of encoding words into numbers is apparently a real thing & I think it is something Gene Roddenberry knew about - an ancient tradition called Gematria https://en.wikipedia.org/wiki/Gematria