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:
Two dwarfs named Brokk and Sindri made a beautiful gold ring for Odin, the chief god. This was a magic ring. The name of the ring was Draupnir.
Every ninth day the ring would reproduce eight new rings of equal quality as Draupnir, the original ring.
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But this does not explain the significance of the non-prime number 9 in LoTR. I will hazard a guess; pure speculation, though I will provide some basis for my guess. The number 9 is a departure from the primes, which represent mysticism, the magic and mythology of the Elder Days. The number 9 departs from the primes because it represents a watershed juncture in Tolkien's mythos; the passage of the Elder days and the coming of the ascendency of Man.
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:
Tall ships and tall kings
Three times three,
What bring they from the foundered land
Over the floundering sea?
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Three times three, nine again. Representing the coming of the Kings of Men to Middle Earth and the end of the Elder days, the days of magic and myth.
Thoughts?