There is no formula for the computation of prime numbers. Each number must be examined individually to determine whether it is a prime or non-prime (also known as a composite number). The largest prime number is currently the 48th Mersenne Prime and it was only recently found. Mathematicians have noticed what appears to be a "fuzzy" pattern in the sequence of primes. It was the search for a method to determine whether there was in fact a pattern that lead Stanislaw Ulam to conceive of a two-dimensional spiral of numbers as a means to provide evidence of a pattern that could lead to a formula for its computation. In the process, it was noted that there was indeed a pattern and that the pattern bore an unmistakable connection to quantum mechanics. However, the appearance of this pattern was inconclusive. That is to say, it could not be proven one way or the other.
We would only add that with a knowledge of God's Name and its abbreviations, there is not only a pattern to the sequence of primes, but that pattern is quite literally an extension of the mathematics of the cube of creation defined by the letters in the Name, and we will here endeavor to show that this is in fact the case, by using the Ulam Spiral as the basis for the assertion.
In order to understand the implications, we must first examine several methods of testing for patterns. One method is to take a one-dimensional string of data, map it in two dimensions and then look for visual patterns that might otherwise be non-computational (patterns for which there is no mathematic formula). For example, create a two-dimensional grid that consists of 10 numbers by 10 numbers1, and then look for repeating sequences that take the form of diagonals, or pairs, or triplets. By using this method, there do appear to be what might be patterns in the list of primes ('might' being the operative word). However, the results at this level are (were) statistically inconclusive.
Ulam reasoned that it might be possible to test the theory (e.g. determine whether there was 'order' to what might otherwise appear as 'chaos') by creating a two-dimensional matrix in the form of a spiral. The Ulam Spiral as it came to be known, is shown below, and the primes within the spiral are shown in the diagram that follows.
The fact that there are clearly defined diagonals suggests that there may indeed be some kind of order (pattern) to the sequence of primes, but again, at this level, any statistical analysis was and is still inconclusive, and there is no computer program capable of determining otherwise.
The human mind however is nevertheless capable of seeing something (like a pattern) that a computer/statistical analysis cannot discern. When this spiral is expanded to 262,000 primes (plus or minus) it looks something like the next picture you see below. Again, a computer (program) would have no way of determining the existence of a pattern. Why? Because in this case, the pattern consists of fuzzy clusters, where each component (in its exact position) is slightly different from that of any potential counterpart, and thus non-computational. The human brain however, is capable of rising above this limitation, and can easily see what otherwise is impossible to ascertain (except with perhaps a quantum computer that does not yet exist).
Examine the pattern of primes (shown in black) against non-primes (shown in white) in the spiral below, and note the fuzzy pattern that emerges. Then using your knowledge of the letters in God's Name; or more specifically its abbreviated forms; and the nature of the marriage between the letters as explained in the post on that topic, test the theory yourself. Assuming you've read these essential constructs to the right, and specifically the one on the marriage of the letters, the geometry in the pattern below should be immediately recognizable.
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If you've not yet made the connection, or are unable to discern the correlation between the letters and the pattern created by the mapping of the primes against the non-primes, we'll use the 'fuzzy' constructs that emerge from the sequence of primes, and pair them with their appropriate letters, as a function of the two (and eventually three) primary abbreviations of the Name. Note first the symmetry of the four "couples" that are four opposite four.
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Eight elements in a pattern could easily be a coincidence, but what if these elements were only part of a more complex pattern that was found repeatedly, not only throughout the Torah, but the physics of time and space, quantum mechanics etcetera? Indeed the above pattern and the letters shown, reflect only a portion of the pattern in the Ulam Spiral, the balance of which is also closely related, if not identical to a two-dimensional orthographic projection of a three-dimensional star tetrahedron, which is in turn associated with the 216 letters of the One Unique Explicit Name. For purpose of this "test" we'll overlay the two-dimensional elements of the three-dimensional star tetrahedron on top of the pattern to reveal the full geometry of the Name within the fuzzy constructs that emerge from the Ulam sequence of primes:
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The structure in the sequence of primes that can be seen in the Ulam Spiral, is indeed a two-dimensional orthographic projection of the tetrahedral geometry associated with the letters that also happen to coincide with certain aspects of quantum mechanics (as already noted by physicists) but perhaps this too is a coincidence.
We do see a pattern consistent with the marriage between the four opposite four (the four letters of the Tetragrammaton opposite the four letters of Adnoot) and also tetrahedral geometry. But how far does it go? And is it a coincidence? What about the marriage of the letters that results in another four? Study the pattern closely before continuing. Can you see the resulting four?
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In the pictures above and below, we have not only labeled these four elements of the Ulam pattern to show that it remains consistent with the marriage of the Tetragrammaton and Adnoot that result in the four letters of the composite (alpeh-heh-yud-heh) but in the picture below, we have overlayed an orthographic projection of star-tetrahedral geometry to show that it remains consistent with the marriage of the two opposing halves in a star tetrahedron (all eight opposing triangular halves).
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In the first picture (above) the four letters of the Tetragrammaton are shown in blue, the letters of Adnoot are shown in red, and the letters of Ehyeh (the marriage of the two) are shown in green (on top of the additional four circular clusters of primes in the outer part of the pattern). The tetrahedral structure that emerges from the underlying nature of the Ulam Spiral is hidden within the limitations of two-dimensional space, but nevertheless present.
In the second picture (below) the pattern, as it relates to the letters, is depicted differently (for purpose of visual experimentation) but the geometry is essentially the same. In this example, the four letters of the Tetragrammaton are again shown in blue, the letters of Adnoot again shown in red, and the letters of Ehyeh (after marriage) are shown larger in green (the circular clusters of primes can be seen at the top of the triangle which has been added to draw your attention to these four additional clusters). The tetrahedral pattern that emerges from the underlying nature of the Ulam Spiral is again present, only in this case the four outer two-dimensional halves of the three-dimensional magen david are external to the four (remaining) inner two-dimensional halves of the magen. You can envision the pattern any way you want, however the pattern is unmistakable, and clearly a function of the Name that defines reality, whether it be the duality in the four forces of quantum mechanics or the duality in the four dimensions of the observable universe. Each is a reflection of a larger reality defined by the cosmic blueprint (combined cubic form of the luchot) which is in turn defined by an even larger reality, which is the letters of the Explicit Name. There is a fuzzy connection between the sequence of primes, the mathematic aspects of the cosmic blueprint (combined cubic form of the luchot) and the letters of the Name. But why is the connection fuzzy? Or to be more precise, why are the patterns created by the primes not identical with one another? Why the subtle variation in composition?
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It is my opinion, that the slight differences we see between the various constructs in the primes of the Ulam Spiral (its fuzzy nature) represent the unique energy signature associated with each of the corresponding letters. The concept of these letters being representations of primordial energy was advanced by the Sages of Israel, who knew how to combine and permute the letters for various purposes.
Either way, we have in the sequence of prime numbers, yet another glimpse of the interconnectedness between the luchot; God’s Name; and the physics and chemistry of everything else in the physical and nonphysical universe. All have this unique inexplicable mathematic and geometric connectedness that defies logic. The numbers, sets of numbers and the ratios between sets, together with what they represent in terms of complex two or three-dimensional geometry, are like an unmistakable fingerprint that hides the very real fact that the letters of God's Name, hidden beneath the surface of so many things, do indeed define our very existence.
Click here to read the next advanced construct on: String Theory and the Luchot
Footnote 1 - This is how R. Weissmandl tested/discovered "Torah Codes" in the form of equidistant letter skips.