By 1997, Hubble Telescope was in full operation, and with this expanded view of universe, conclusion became that "something"--some kind of energy--has been continually rushing into universe, pushing galaxies apart. It was dubbed "Dark Matter" because it couldn't be seen or measured, only deduced. This Dark Matter theory began explaining things in strange new ways for modern physicists, who were concluding that up to 95% of mass of universe couldn't be accounted for--an embarassing situation for many scientists...

However, these conclusions opened up huge possibilities for understanding and verification of many forms of ancient medicine, as well as early theories about how universe was formed and how matter is created. Enter Dr. Yury Kronn.

After spending nearly 20 years deep in research into quantum mechanics and dark matter, and serving as a professor at Moscow University, Dr. Kronn began to feel constrictive effects of Soviet on his work, as well as work of his colleagues. In 1982, Dr. Kronn, together with ten other Russian dissidents, organized "Trust Group," first independent movement in history of Russia for Trust and Peace between Russia and Western world. In 1987, Dr. Kronn was again part of Russian history when he chaired Disarmament Section of first Moscow International Symposium for Humanitarian Problems, which was broadcast around world. The KGB and Russian authorities persecuted him for his social activities. Finally, he was able to immigrate as a political refugee to U.S. in 1988. Dr. Kronn arrived in United States to start a new life with only a suitcase and $150.

Still on his mission to export his knowledge for good of humanity, Dr. Kronn's immediate application of his research was in medicine. With U.S. alternative health business booming, Dr. Kronn found many eager ears for his theories and his work, and soon was able to construct Subtle Energy Field Infusion Generator (SEFIG).

The SEFIG had unique ability to separate "dark matter" or subtle energy from electromagnetic energy residing in any substance. It was able to extract and "save" this subtle energy "signature" and then generate this signal and infuse it into any object. Associations with alternative medicine practitioners, medical doctors and scientists, provided ample opportunity to test effects of this subtle energy infusion on people. "You know that traditional Chinese medicine and philosophy use term 'Chi' for energy which, according to them, sustains life in all living organisms," says Dr. Kronn. "Indians use term 'Prana' for this same universal force. Actually each culture has its own term for this force. My technology is based on equipment that allows access to world of that mysterious force we call subtle energy."

Another Dr. Kronn breakthrough was discovery of different sub-divisions, or frequencies, within subtle energy domain. In fact, he found that any substance had its own subtle energy signature. Additionally, by borrowing from ancient modality of acupuncture, Dr. Kronn was able to extract energetic signatures of human acupuncture meridians, and infuse this energy into an ingestible substance, such as an ionic mineral solution. Says Dr. Kronn, "We print vital energy patterns onto magnetic tapes, infuse them into liquid trace minerals, crystals, oils and creams. Energy patterns can be infused into any substance capable of storing information. These energy infused substances serve as delivery tools of patterns to human energy system. We call them 'energy tools.'"

Randomness and Prime Twin Proof

Martin C. Winer

martin_winer@hotmail.com

Referring sites: I’m greatly appreciative of sites that have found my work interesting and have linked to me: Most Notably, I appreciate:

Google Directory Google Prime Directory DMOZ Open Directory Project DMOZ Open Directory H. Peter Aleff @ recoveredscience.com Recovered Science

Introduction Overview The purpose of this work is to look into some long pondered questions. First, is distribution of primes across number line random? Next, what is random anyways? Finally theories and axioms derived are used to solve long discussed “Prime Twin Problem” to show possible applications of understanding of what it means to be random.

Sieves and Patterns Consider all odd numbers starting at 3.

Mark a 1 on number line where number is a product of 3, (including 3x1), 0 otherwise. We get a pattern (sieve) such as:

1 0 0 1 0 0

3 5 7 9 11 13

1)The pattern is 100...

2)Note that numbers corresponding to zeros between 3 and 3^2=9 are also prime (5 and 7).

3)The length of pattern is 3

Consider pattern formed by 3 and 5:

1) pattern is 110100100101100...

2) Note that numbers that correspond to zeros between 5 and 5^2=25 are also prime (7,11,13,17,19,23)

3) The length of pattern is 3x5=15

Definition of P(x) [The Xth Prime] In general

If we let P(x) be xth prime starting from 3 such that

P(1)=3, P(2)=5, P(3)=7 and so on, we can consider patterns on a larger scale.

Definition of Pat(n) Suppose we define a function Pat(n) which will produce string of ones and zeros as defined above from P(1) to P(n).

I.e. Pat(1) = 100…

Pat(2) = 110100100101100… (That’s pattern or sieve of 3 and 5)

In such a case,

(1) The pattern will consist of 1's and zeros corresponding to products and non-products of n composing prime factors,

(2) The numbers corresponding to zeros between P(n) and P(n)^2 are guaranteed to be prime

[Why? because a number is either a prime or a product of primes. A zero means that it's not product of any prime below it. The first unique contribution a prime factor gives to number line occurs at P(n)^2 = P(n)xP(n) because below that at say P(n)xP(n-1) can be rewritten as P(n-1)xP(n) and thus is already accounted for in number line. Thus a zero between P(n) and P(n)^2 is not a product of primes and must therefore be prime.]

(3) The length of pattern will be:

P(n) x P(n-1) x P(n-2) x ... x P(1)

Unique Contributions of P(x) Description As we build iteratively build Pat(n)’s over time, each successive prime adds to our knowledge of which numbers are prime and which numbers are not. In case of prime number 3, we know that 3 is prime and that all (other) multiples of 3 are not prime. However, when we come to prime number 5, 5 does not ADD to our knowledge that all multiples of 5 are not prime. For example 15 is a multiple of 5, but we already knew that this number was not prime because of prime number 3. Therefore, unique contribution to our knowledge as we build Pat(n)’s that a given prime (P(x)) provides us is given below:

Definition uniqueContribution(P(x)) For any prime, P(x), define

UniqueContribution(P(x)) = {P(x)*k; k is odd, k>=P(x), primeFactorization(P(x) contains no primes < P(x)}

In English… The uniqueContribution a prime number (P(x)) gives us as to which numbers are not prime while building successive Pat(n)’s is a function of all odd multiples of P(x) such that odd multiples have no primes less than P(x) in their prime factorizations

Examples: Consider prime 5.

5*5 = 25 is a unique contribution of 5

5* 15 = 5*3*5 = 75 is NOT a unique contribution because it has 3 in its prime factorization. Ie, we already knew that 75 was not prime thanks to prime number 3.

5*5*5 = 125 is a unique contribution.

Powers of a prime It turns out that powers of primes (greater than first power) are unique contributions.

Important Notes on uniqueContribution(P(x)) For larger P(x), uniqueContribution(P(x)) becomes increasingly difficult to calculate and more complicated. The unique contribution becomes more random as P(x) increases.

General Notes on Randomness Axioms of Randomness 1) All truly random patterns must be infinite length

2) A pattern is said to be random if there is an infinite supply of complexity

Black Box Pattern Paradox It can only ever be said that an infinite length pattern follows a pattern for a certain finite length. Suppose you have a machine that spits out 1’s and 0’s and it spits out 1010101010… for a certain number of times you make attempt. You can only say that it follows patter 10… for number of attempts you made because on next attempt, pattern may change. Thus it is impossible to ever say that an infinite length pattern follows a certain pattern unless you are aware of algorithm that generates it.

On Randomness of Primes Measure of Randomness in a Binary Pattern Let’s define a measure of randomness (mr) for a binary pattern to be number of smallest repeating units in lowest reducible pattern.

Definition of Lowest Reducibility: A pattern is reducible if it can be rewritten in a simpler, shorter form, such as:

11111111… is reducible to 1…

10101010101010… is reducible to 10…

Definition of Smallest Repeating Units Take pattern:

Pat(2) = 110100100101100…

This repeats every 3rd and every 5th. Note it repeats every 9th as well but that’s not smallest repeating unit because every 3rd subsumes every 9th. Thus mr of this pattern is 2.

Some Examples for Clarity So,

100000000… is no more or less random than

100…, or

100000000000000000000000…

(Because in all cases mr = 1)

However,

110100100101100… (every 3rd and 5th) is more random than those above since mr=2.

Some other interesting examples for clarity:

110… has mr = 2 because it has two repeating units of size 3, (the second offset by 1)