Tolkien's Numerical Fixation
I know next to nothing about numerology or the mythical significance of numbers. Five minutes of internet research uncovered some distinction between odd and even numbers with one representing male and the other female and a similar light versus dark correlation. I cannot tie this in firmly with Tolkien's works.
However, one thing is very clear. Tolkien had a strong preference, and perhaps attached some significance, to odd numbers in specific, and possibly to prime numbers. For those who do not recall their elementary mathematics, prime numbers are divisible only by 1 and themselves. The first several primes are 1, 3, 5, 7, 11, 13, 19, etc. Tolkien's mythos is replete with an overwhelming quantity of odd numbers, most of which are primes. What follows is a list of what I could think of off the top of my head. Eru, the One. The 3 Themes of the Ainulindale. The 7 kings and 7 queens of the Valar (at least in the published Silmarillion). The 3 Ages of the Elder days. The 3 houses of Elves (having 4 kings, however, until Thingol tarried in Beleriand). The 3 Noldorin princes (Feanor, Fingolfin and Finarfin). The 7 sons of Feanor. The 3 Silmarils. The 3 houses of the Edain. The 7 Fathers of the Dwarves and their corresponding houses. The 7 Gates of Gondolin. The 3 peaks of Thangorodrim. The 5 children of Finarfin and 3 of Fingolfin (in the published Silmarillion at least). 7 (3, 5?) Balrogs. The 7 rivers of Ossiriand (Gelion and its 6 tributaries). The 5 promontories of Numenor. 7 Stones, 7 Stars and 1 White Tree. 3 peaks over Moria. The 5 Wizards. The 7 Gates of Minas Tirith. The 3 Elven Towers on the Tower Hills. The 3 groups or families of the Hobbits. And, of course, "Three Rings for the Elvenkings under the sky, Seven for the Dwarflords in their halls of stone, Nine for the Mortal Men doomed to die, One for the Dark Lord on his dark throne." Up until the Ring Verse, we have all primes, and all numbers on the above list are odd. The exception is the 9 Rings, and of course, their corresponding 9 Ringwraiths and the Nine members of the Fellowship. I wonder whether there is any significance that these are not prime numbers? There are only two exceptions to the litany of odd and prime numbers that are of any real mythological significance in Tolkien's work, at least that I can think of. The 2 Trees and the 2 Lamps of the Valar. Again, any significance here? Then, we have the 13 Dwarves of Thorin's Company and the intentional choice to add Bilbo as the 14th member to avoid the "unlucky" number. No doubt, our members will be unable to resist the temptation to add to these lists, but that is not the point here. Is there any meaning to Tolkien's use of odd numbers (or primes)? Is there any significance to the exceptions; the few even numbers and the odd nonprimes? 
Have to go to class, haven't got time to post longer, but two quick comments:
Quote:
And in general, I think that certain numbers may be chosen because they are "visually appealing". Not in their written form sense, but in the quantity. Even numbers have symmetry. Odd numbers are unpaired. Compare a Magen David to a pentagram  they have a different "feel" based on the visual pairing or symmetry of rays/angles. I think it's the same here. Odd  and especially prime  numbers stand out because they aren't easily grouped (and 9 is grouped in a 3 of 3s, which is also prime and asymmetrical). Great thread, sorry I can't post more, but I gotta run now. :) 
My bad. Of course 2 is a prime. It is the only even prime number, which also makes it stand out.

Back from class and procrastinating on homework by doing an analysis of numbers in literature and mythology as perceived by myself. :p
1 seems to be the obvious one. One. Only one. The one and only. It's something unique and/or special. 2 seems to be used a lot for pairing and comparing. Often there are two things that are juxtaposed. Combinations of two often show either some sort of collaboration or some sort of competition, or "oppositeness". The Two Lamps are like the two poles of Arda the flat. The Two Trees have a bit of both relationships; one one hand, they are paired together, but on the other hand they are given opposite characteristics (gold vs silver). Gondor/Arnor  same story. This is also true for the making of choices and family relationships. You have Hurin/Huor, Turin/Tuor, Elrond/Elros  which are paired and compared, even if not explicitly  and they are connected to each other so strongly with that comparison that sometimes it's hard to think about one without thinking about the other. 3 appears to be used when you want to show equally valid components without necessarily pitting them against each other. Three Houses of Edain and of Elves are good examples. Alternatively, it just seems like an appealing number for things that are rare but not unique  Silmarils, Elven Rings. This might be a matter of taste that was just conditioned into us by past literature, and it keeps getting recycled over and over again as new literature is made. 4 is odd, I think, because though it seems "stable" mathematically (perfect square and all), it tends to fall apart (at least in my mind) into 2 and 2 when a quartet appears in literature. The thing about even numbers is that perhaps I automatically want to pair (which is why 3 seems to be associated with a more stable relationship  you can't split it into independent pairs). But I don't think it's just me. Four hobbits go with the Fellowship, and they are subdivided early on in their travels into the FrodoSam pair and the MerryPippin pair. Four just doesn't seem to be able to hold together. Harry Potter has great examples for both 4 and 3. They have 4 Houses, but instead of being portrayed as equally valid they are split into "Gryffindor vs Slytherin" and "the amity (and relative unimportance) of Ravenclaw and Hufflepuff". On the other hand, the Tale of Three Brothers in the 7th book shows three different approaches, without necessarily showing competition between them, and without grouping anything. I wonder if there is any grouping of four that does not fall apart. I suppose in HP itself there are the four friends of the parental generation, but that relationship is skewed and unequal to begin with; there's one person who sticks out from the start. In the natural world you have the four corners of the world (and in some places the four elements), which should technically be representative of stable quartets, but I can't think of any examples at the moment. The Greeks even had just three winds, ignoring the East Wind completely, if I remember correctly. Thoughts? There's something appealing about small odd numbers. 5, 7, 9 are, in my opinion, chosen less for their own merit than as a means of avoiding the more boring 6 and 8. There's nothing wrong with either of them, but odd numbers just seem more satisfactory. (Compare the number of trilogies and 7book series to the number of series with a different number of books. 4 and 5 occur occasionally, but I've yet to see a 6 or an 8). You can't group things into equal portions with 5 and 7, and 9 is broken into a 3 of 3s. These numbers seem to be more like 3 and less like 4, though they still could be broken down into uneven segments. It's interesting that if a larger number is of a homogeneous thing, it's more stable, but if there are differences than it breaks apart into smaller groups. I've got no problem with 9 Nazgul, but some area of my brain feels the need to subdivide the Fellowship into smaller groups. Gandalf of course has a group all for himself. The Men seem to be paired and even have a subtle competition going on. Perhaps it's in the way they are described (e.g. "Boromir was wider, but Aragorn was slightly taller" (paraphrased)), or perhaps it's just me; when I read LOTR as a kid, Aragorn was my favourite character, and I was indignant any slight to him. I would get indignant when the book said Boromir killed more orcs than Aragorn. I guess I felt the need to justify my favourite character, and any equal seemed like a rival. But moving on. Legolas and Gimli are paired by virtue of being the "weird foreign people/races", and then they develop their unusual relationship, and basically by Lorien they are a character couple. That leaves the four hobbits as a group  but as I mentioned before, that number seems to fall apart too. Perhaps a lot of this is our tendency to categorize things. Perhaps it's not that we (or authors) choose to group things a certain way to show something with the use of numbers, but rather the reason we see something in numbers in the first place is because of the relationships in these preexisting categories; we perceive first, and count later, but then we think it's the number that influences what we perceive. A lot of it has to do with conditioning  you read a book where the number 3 holds some significance, and you generalize that feeling to other trios. Well, that was food for thought, but thoughts for food are hardly as good of an offer. Lunch! 
Of course Tolkien had a Numerical fixation. He was, after all, Numenorean.

Galadriel55, a worthy effort.
Morthoron, not so much. ;) I have done some research and have found little to explain what appears to be an intentional pattern, though others have commented upon the numerical implications in LoTR. The significance of prime numbers is a bit obscure. The Greeks considered them mystical because they were randomly placed within the succession of numbers, and represented chaos. The symbolism of number one is simple. It represents primacy; the deity. The applicability of number one to Eru is obvious. The applicability to the One Ring and Sauron appears to be the desire for primacy and to become the deity. What I cannot clearly understand is Tolkien's deviation from the use of prime numbers regarding the 9 mannish Rings (and 9 Wraiths) and the 9 members of the Fellowship. I can suggest a source for the 9 Rings ( and others more deeply steeped in Norse mythology can supplement). There is a myth regarding a ring owned by Odin. I quote an excerpt from the website mysticalnumbers.com. Quote:
The number 9 is found in the number of mannish Great Rings, the number of Ringwraiths (all men), and the number of members of the Fellowship, the persons assembled to via against Sauron and bring about the fall of the Ring and its master (bringing the Elder Days to their close). To this collection of Nines, I will add another. Quote:
Thoughts? 
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