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Thread: Prime numbers

  1. #1
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    Prime numbers

    Hi folks! Thought I'd give some brief data re prime numbers from the first verse of the Bible.

    Mathematicians universally recognise the number 2 as the first of the primes. This is as it should be, as the number 1 is far too special to be lumped in with the prime series. The number 1, referred to as unity, is the only indivisible integer. All the primes are divisible by 1, making them all dependent on 1 for their existence. In a similar fashion, all composite numbers are divisible into primes. There is a hierarchy at play amongst numbers, which may be divided into three categories: (a) Unity, (b) the primes, and (c) the composites. As with the Godhead, numbers themselves are organised around tri-unity.

    The first letter of Scripture is the Hebrew 'beth', equivalent to our b, which has a numerical value of 2. This letter begins the first word, 'bereshith', and is always written larger than other letters in Genesis 1 in the Hebrew scrolls. Appropriately, Scripture begins gematrically with the first prime number. Just as the primes lead us into all combinations of numbers, so the 'beth' leads us into the word of God.

    The subject of the Bible's first verse is God, the Hebrew 'elohim'. This word has a numerical value of 86. Anyone who has followed Richard's work knows that there is a strong numero-geometrical link between the thematically related verses of Genesis 1:1 and John 1:1. Both verses open with the phrase: "In the beginning ...". The subject of John 1:1 is the Word, in Greek 'ho logos'. The Word - 'ho logos', which context shows us to be none other than the Lord - has a numerical value of 443. 443 is the 86th prime number.

    The prime index of 'ho logos' links to the 'elohim' of Genesis 1:1. They both share a relationship through the number 86. In this way, gematria shows us that the thematically linked subjects of both verses are, in fact, the same being. Jesus Christ is, indeed, the Creator of the heavens and the earth.

    This is a very simple lesson in relation to prime numbers. Genesis 1:1 contains many such lessons in relation to the primes, although this is probably the simplest of them all. It should not escape our notice that the prime factors of Genesis 1:1 have a reflexive property through the pair 37 and 73. This is undergirded by their prime indices, 37 being the 12th prime and 73 the 21st prime.

    I hope this morsel might inspire others to consider the role gematria plays in Scripture.

  2. #2
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    Outstanding Stephen! Also beginning in Genesis 1:1, counting each letter "Aleph" we find that this first letter of the Hebrew alphabet, who's number is 1 and indicates God, appears 6 times, man's number. If we count from the first letter, the oversized Beth, 86 letters, we find the letter "Aleph". We can do this with the Gematria of God's other "names" and find the same thing. Yah is 15, YHVH is 26, God (EL) is 31, try this for yourself. God's word is as complex and carries the same intelligent design as all of His creation.

  3. #3
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    aleph

    Yarah, fascinating observation in regards to the 'aleph' and its recurrence as the 15th, the 26th, the 31st and the 86th letter of Scripture. As you remark, these are the gematrical values of the key OT names for God.

    God Himself declares His sovereignty in the Shema by announcing that He is One. Aleph being equivalent to 1, and the Hebrew for one being 'echad' (probably related to our English word 'accord') - which word begins with aleph - it is of further interest that aleph has a gematrical value of 111. There is a clear indication that the number 1 is not to be likened to any other number, that it stands apart from, and over, all numbers in the same way that God stands apart as the first cause, over all creation.

    In relation to aleph in Genesis 1:1, you are probably already aware that the nominal positions of each of the six alephs in the verse sum to 86. Naturally, it goes without saying that 'elohim' begins with aleph.

    I am reminded, too, of the acronym for God's great name: 'ehyeh esher ehyeh'. All three words begin with aleph, marking this letter as peculiar to God.

    The origins of the letter aleph apparently lie in the pictogram of the head of an ox. In the ancient palaeo-Hebrew script, the protean aleph's form resembles uncannily that of the stars in the head of the constellation Taurus. There is every likelihood that the stars themselves are the origin for both the name and the form of this letter.

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    Primes vs. Numerical Atoms

    Quote Originally Posted by Stephen View Post
    Hi folks! Thought I'd give some brief data re prime numbers from the first verse of the Bible.

    Mathematicians universally recognise the number 2 as the first of the primes. This is as it should be, as the number 1 is far too special to be lumped in with the prime series. The number 1, referred to as unity, is the only indivisible integer. All the primes are divisible by 1, making them all dependent on 1 for their existence. In a similar fashion, all composite numbers are divisible into primes. There is a hierarchy at play amongst numbers, which may be divided into three categories: (a) Unity, (b) the primes, and (c) the composites. As with the Godhead, numbers themselves are organised around tri-unity.
    Stephen,

    I like the mathematical clarity and integrity of your presentation. Some years ago I met a man who believed the primes should start at 1. It might seem like a trivial matter, but it actually is of central importance if we are looking for correlations between the prime and its index. Since the mathematical properties would not allow me to think of unity as a prime, I invented the idea of "numerical atoms" which are just the union of unity with the set of primes. Then I compared the correlation between the numerical atoms and their index versus primes and their index.

    There were a number of interesting "hits" with the atoms. For example, it is pleasing to have a perfect correspondence between the first three atoms and their indexes (1/1, 2/2, 3/3) as opposed to the heterogeneous mix that primes have with their indexes (1/2, 2/3, 3/5). On the other hand, heterogeneity is very fertile and full of "dynamic tension" that goes somewhere and develops, so perhaps the primes are to be preferred over the atoms.

    Another satisfying correlation in the "atoms" list is that the number 13 is the 7th "atom", so we have a correlation between Hex(2) = 7 and Star(2) = 13, the second Hex/Star pair.



    A similar hit is that the Number 37 is the 13th "atom" which are both star numbers. Likewise, the Number 151 is the 37th "atom", and 151 = the heart of the Logos Star 373 = 6 x 37 + 151.

    BUT ... there also are some powerful hits starting with 2 as the first prime. As you noted, we have the correlation between the prime 443 (Ho Logos) and its index 86 (Elohim). Likewise, we have a correlation between the very significant prime 613 (YHVH Elohi Yisrael) and its index of 112 (YHVH Elohim).

    We also have a correlation between the 114th Prime = 619 which is the large prime factor in the Grace Manifest Holograph that is indexed by the number 114 (John 1:14). This is particularly interesting because now we have a verse of the Bible indexed by the index of the large prime found in its gematria!

    I think that following the standard mathematical practice makes sense and is very elegant, especially in light of its threefold structure of Unity, Primes, Composites. This seems confirmed by the integration with the names of God, which I didn't find in the "numerical atoms" list. But the geometric correlations in the "atoms" makes me wonder if something is going on there.

    But I find it difficult to discern between chance and design in this case, so I will remain uncommitted for now.

    Thanks for the great post!

    RAM

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    I was thinking about how some of the more "skeptically inclined" might mock the idea that God could have anything to do with patterns in primes, since the patterns seem like they had to be established by their very nature, so that even God had no choice in the matter.

    Then I remembered that Carl Sagan, a skeptical egghead frequently quoted by atheists, wrote a very entertaining book called "Contact" in which he suggested that the Creator had encoded the digits of Pi so that when they are displayed in a certain way the zeros would form a perfect circle, which relates back to the definition of pi, and so forms a kind of message from the Creator.

    Carl's suggestion caused some controversy because Intelligent Design folks quote him in support of their position. Here is a bit from Wikipedia:

    Intelligent design proponents often cite the ending of Contact as proof that Sagan believed that, using the tools of science, it was possible to discover if there was a creator of the universe. This interpretation is in direct conflict with the vast body of Sagan's views as represented in his work and writings. Such as The Demon-Haunted World as well as Science as a Candle in the Dark, of which are skeptical about claims of supernatural origins of the cosmos and favor explanations of a naturalistic origin.

  6. #6
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    atom numbers

    Hi Richard,

    I am familiar with your concept of the 'atom numbers'. Mathematicians refer to these as irreducible numbers, being the prime series prefixed by unity. They produce fascinating results at times, and the series is not without merit. I regard them as a useful supplement to the prime series, but not a replacement for them.

    Like yourself, I had given much thought to whether or not the number 1 deserved to be called prime. In the end, logic dictated that the mathematical community were correct in their conclusion that 1 is not prime. In a philosophical kind of way, mathematicians have affirmed that there is nothing else like the number 1. In the same way, we know that there is nothing else like God, who calls Himself One in the Shema. I'm sure you can make the connection.

    I apply the law of Occam's razor in this instance to prove that 1 is not prime: all the prime numbers are divisible, but 1 is indivisible. Applying this to your concept of 'atoms', we may conceptually divide the atoms one from another in a compound and represent these in a diagram of chemical structure. However, we cannot of itself split a single atom; to do so would be to obliterate its atomic entity. It would no longer be a single atom.

    Quite simply, God is not divided in Himself.

  7. #7
    Quote Originally Posted by Stephen View Post
    ... as the number 1 is far too special to be lumped in with the prime series. The number 1, referred to as unity, is the only indivisible integer. All the primes are divisible by 1, making them all dependent on 1 for their existence.
    Stephen, I really like your post, because it causes me to consider the spiritual implications from what you have stated.
    Here's a little more food for thought...

    In Mark 12:29, Jesus is quoting from Deuteronomy 6:4, stating... "Hear, O Israel: the LORD our God is one LORD:"
    The triune nature of God as three persons in One being is more clearly understood when we look to One as the answer.
    Our great and marvelous God is a God of abundance and multiplicity. When people look to addition 1 + 1 + 1 = 3,
    they get stuck because 3 does not equal one.

    For me, this mathematical sequence expresses the trinity (how God is One): 1 X 1 X 1 = 1
    The three persons of one Father forever multiplied to and by the one Son forever multiplied to and by the Holy Spirit.
    God therefore, being unity, is indivisible, and we too, like the numbers you refer to, are dependent on (unity);
    the One true God for our existence.
    Love, in Christ, and all for His glory!

  8. #8
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    Quote Originally Posted by Triple Nine View Post
    Quote Originally Posted by Stephen View Post
    Hi folks! Thought I'd give some brief data re prime numbers from the first verse of the Bible.
    Mathematicians universally recognise the number 2 as the first of the primes. This is as it should be, as the number 1 is far too special to be lumped in with the prime series. The number 1, referred to as unity, is the only indivisible integer. All the primes are divisible by 1, making them all dependent on 1 for their existence.
    I think you are correct that the agreement now is near universal, and I think the reasons you gave - which are based ultimately on Algebraic Number Theory, are also correct. But historically there has been some debate about the prime status of the Number One. An interesting series of answers to the question "Why is One not a Prime", which seems to cover most possibilities, is found here: http://primes.utm.edu/notes/faq/one.html

    The first two answers he gives seem pretty weak and unconvincing. The first is based on the definition of a prime:

    "An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself."

    But that proves nothing because we could just as well define a prime as "A positive integer is called a prime number if its only divisor (factor) greater than one is itself. "

    The second reason listed is also inconclusive because it too is based on an arbitrary definition in the Fundamental Theory of Arithmetic:

    "Every positive integer greater than one can be written uniquely as a product of primes, with the prime factors in the product written in order of nondecreasing size."

    We could simply reword this theorem to state:

    "Every positive integer can be written uniquely as a product of primes greater than one, with the prime factors in the product written in order of nondecreasing size."

    Obviously, there must have been some other reason(s) that mathematicians would go against the strong natural inclination to include one with the primes. And indeed there is, as we begin to see in the third reason listed on the primes page. It explains that One is not a prime because it is a "divisor of unity."

    And finally, his fourth reason pretty much settles the issue as far as I can tell:

    There was a time that many folks defined one to be a prime, but it is the importance of units and primes in modern mathematics that causes us to be much more careful with the number one (and with primes). When we only consider the positive integers, the role of one as a unit is blurred with its role as an identity; however, as we look at other number rings (a technical term for systems in which we can add, subtract and multiply), we see that the class of units is of fundamental importance and they must be found before we can even define the notion of a prime. For example, here is how Borevich and Shafarevich define prime number in their classic text "Number Theory:"
    An element p of the ring D, nonzero and not a unit, is called prime if it can not be decomposed into factors p=ab, neither of which is a unit in D.
    Sometimes numbers with this property are called irreducible and then the name prime is reserved for those numbers which when they divide a product ab, must divide a or b (these classes are the same for the ordinary integers--but not always in more general systems). Nevertheless, the units are a necessary precursors to the primes, and one falls in the class of units, not primes.
    As discussed earlier, this issue is very important to some folks who feel that the patterns found in the relations between primes and their indexes proves that one is a prime. But for that purpose, we could just adopt a new class of numbers - Atoms as Stephen mentioned - and let the mathematicians keep their prime definition pure, since intellectual purity is a prime passion of mathematicians, I can assure you!

    That's why Christians are often excellent mathematicians. E.g Blaise Pascal (Probablitiy theory), Isaac Newton (inventor of Calculus.

    RAM

  9. #9
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    Agreed

    Hi Folks!

    I am in perfect agreement with Richard. The primes ought to remain as they are, while the prime series supplemented by the addition of 1 should be given a new name. This latter series does have some interesting findings; however, I regard it as a secondary source of information in relation to the prime series. Triple Nine mentioned some of the philosophical implications of 1 being in a numerical class of its own, relating these to the Godhead. I am in perfect accord with those conclusions.

    Stephen

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    prime numbers

    Quote Originally Posted by Stephen View Post
    Hi folks! Thought I'd give some brief data re prime numbers from the first verse of the Bible.

    Mathematicians universally recognise the number 2 as the first of the primes. This is as it should be, as the number 1 is far too special to be lumped in with the prime series. The number 1, referred to as unity, is the only indivisible integer. All the primes are divisible by 1, making them all dependent on 1 for their existence. In a similar fashion, all composite numbers are divisible into primes. There is a hierarchy at play amongst numbers, which may be divided into three categories: (a) Unity, (b) the primes, and (c) the composites. As with the Godhead, numbers themselves are organised around tri-unity.

    The first letter of Scripture is the Hebrew 'beth', equivalent to our b, which has a numerical value of 2. This letter begins the first word, 'bereshith', and is always written larger than other letters in Genesis 1 in the Hebrew scrolls. Appropriately, Scripture begins gematrically with the first prime number. Just as the primes lead us into all combinations of numbers, so the 'beth' leads us into the word of God.

    The subject of the Bible's first verse is God, the Hebrew 'elohim'. This word has a numerical value of 86. Anyone who has followed Richard's work knows that there is a strong numero-geometrical link between the thematically related verses of Genesis 1:1 and John 1:1. Both verses open with the phrase: "In the beginning ...". The subject of John 1:1 is the Word, in Greek 'ho logos'. The Word - 'ho logos', which context shows us to be none other than the Lord - has a numerical value of 443. 443 is the 86th prime number.

    The prime index of 'ho logos' links to the 'elohim' of Genesis 1:1. They both share a relationship through the number 86. In this way, gematria shows us that the thematically linked subjects of both verses are, in fact, the same being. Jesus Christ is, indeed, the Creator of the heavens and the earth.

    This is a very simple lesson in relation to prime numbers. Genesis 1:1 contains many such lessons in relation to the primes, although this is probably the simplest of them all. It should not escape our notice that the prime factors of Genesis 1:1 have a reflexive property through the pair 37 and 73. This is undergirded by their prime indices, 37 being the 12th prime and 73 the 21st prime.

    I hope this morsel might inspire others to consider the role gematria plays in Scripture.
    Hi Stephen,

    I like to say something about the prime numbers, but I think it makes sence to say something about numbers in general, so we can understand the number universe of God. There are infinit numbers build up out of 9 digits (the zero is not a digit) So we have:

    1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9
    the building blocks are:
    (1)-(1+1)-(1+1+1)(1+1+1+1)-(1+1+1+1+1)-(1+1+1+1+1+1)-(1+1+1+1+1+1+1+1).......
    or
    (1)-(1+1=2)-(2+1=3)-(3+1=4)-(4+1=5)-(5+1=6)-(6+1=7).......

    We can divide the infinit numbers in many different ways. The first logic way are the triangular/not triangular numbers:

    1-(1)-(1+2=3)-(1+2+3=6)-(1+2+3+4=10)-(1+2+3+4+5=15).......

    So 1 is the first triangular number, 3 the second, 6 the third, 10 the fourth and so on.....(I think we don't have a word for numbers that are not triangular)

    An other division of nubers is odd and even:

    1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.......

    number 1 - 2 - 3 - 4 - 5 - 6 - 7 .......
    0dd 1 - 3 - 5 - 4 - 7 - 9 - 11 - 13 .......
    Even 2 - 4 - 6 - 8 - 10 - 12 - 14 .......

    So the first odd number is 1 and the first even number is 2; the seventh odd number is 13 and the seventh even number is 14.

    We can also divide the numbers in primes and composites:

    1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 -10 - 11 - 12 - 13

    number......1 - 2 - 3 - 4 - 5 - 6 - 7 ......
    prime.........1 - 2 - 3 - 5 - 7 - 11 - 13 .......
    composite.. 4 - 6 - 8 - 9 - 10 - 12 - 14 .......

    This makes in my opinion 1 as the first prime and 4 as the first composite. There is no reason to treat the one in a different way in the sequence of primes than in the sequence of triangular or odd numbers. And yes one is a very special nuber as a unity. But the three and the seven are also very special. You can see in the sequence of primes that the first three primes are equal to their numerical place; so in heaven, so on earth. That's why I call them Super Perfect Primes. The highest number in this 'world' is the three. The three raised till its own power is 3x3x3=27, the starting point of the number of letters of the Hebrew alphabet, including the sophit letters. In this sequence of 27 numbers we find 10 primes. These 10 primes in the sequence 'n' appoint in the prime sequence 10 other primes, of which the first three are the Super Perfect Primes and the other seven I call Perfect Primes. You can find more informatin on the following pages:
    http://members.home.nl/frankcolijn/f...n/6._Truth.htm
    and http://members.home.nl/frankcolijn/f...rime_table.htm

    I think it is interesting to know that the sum of the 10 primes in the sequence 'n' (27) and the 10 Perfect Primes is: (1+2+3+5+7+11+13+17+19+23)+(1+2+3+7+13+29+37+53+61 +79)=101+285=386, the Hebrew CV of Jesus.

    I hope that this information adds something to the prime discussion, Frank
    Last edited by Frank Colijn; 08-06-2007 at 07:27 AM.

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