8/6/2010 Justin Coslor
Prime Experiments
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In the Natural Number System,
Given:
All prime numbers (with the exception of the number 2) are odd.
All odd numbers are only divisible by odd numbers.
All even numbers are divisible by 2.
Therefore:
Duplicates produce the only instances of even numbers.
The rest are all odd numbers multiplied by odd numbers, including prime
numbers other than 2.
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Check every integer for how many prime divisors it has.
Is there a pattern about how many prime divisors a prime number
neighborhood midpoint has?
(PNN = Prime Number Neighborhood)
PNN midpoints are sometimes even and sometimes odd.
1. Midpoint for PNN spacing of size S always has at least d prime divisors
and at most D prime divisors. True/False?
2. Midpoint for PNN spacing of size S always has exactly P prime divisors.
True/False?
3. What PNN spacings have any common midpoint divisors besides twin primes
(midpoints divisible by 2)?
// 4. When Even Midpoints of (PNN + 2N) = Even PNN Midpoints,
// Then the midpoints are always divisible by the prime number 2.
// When Odd Midpoints of (PNN + 2N)
5. Non-prime odd numbers always have two or prime divisors common divisors
and no even number divisors. That also holds true for PNN midpoints.
6. Do prime numbers exist in any number system other than the Natural
Number System, and if so do they exist in a different way in those other
number system structures?
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8/7/2010 Justin Coslor
Prime considerations.
http://justin.freeshell.org/11-04-2009-ADDITION-CHART-POSSIBILITIES.TXT
[3:13:48 PM] Justin M Coslor:
http://justin.freeshell.org/20100730-Rope-Folds.jpg
[3:14:37 PM] Justin M Coslor: http://justin.freeshell.org/midpoints.txt
[3:17:41 PM] Justin M Coslor:
http://justin.freeshell.org/11-24-2009-ADDITION-CHART-POSSIBILITIES-QUIZ.TXT
[3:22:56 PM] Justin M Coslor: Are composite numbers cross domain relations
of prime numbers? What about prime numbers represented each in the base
prime that that number is?
[3:23:29 PM] Justin M Coslor: Like 3 represented in base 3 and 5
represented in base 5 and so on.
[3:23:46 PM] Justin M Coslor: What about binary and base infinity?
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8/7/2010 Justin Coslor Prime Test
[3:52:23 PM] Justin M Coslor: If N is any Natural Number up to P^(1/2),
then P is prime when N/P = 1/P. P^(1/2) = square root of P.
[3:57:33 PM] Justin M Coslor: and N/P = 1/P means P is only prime when N =
1
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8/7/2010 [3:45:40 PM] Andrew Dougherty:
On properties related to prime numbers.
(is-odd ?N)
(is-even ?N)
(has-midpoint ?P1 ?P2 ?M)
(has-spacing ?P1 ?P2 ?S)
(is-power-of-2 ?N)
(is-divisible-by ?N1 ?N2)
(is-prime ?P1)
(methods to prove primality)
(methods to filter for possible primes)
(methods to efficiently reject prime candidates
(is it even)
)
[3:48:37 PM] Andrew Dougherty: (implies
(is-prime ?p1)
(not
(exists ?n
(and
(is-divisible-by ?p1 ?n)
(or
(equals ?n ?p1)
(equals ?n 1))))))
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8/7/2010 Justin Coslor
Is this a potential prime number generator?
primeA + primeB = primeN +/- 1
Meaning that if this is true,
then when two sequential prime numbers are added together,
the sum is always equal to some larger prime number plus or minus one,
for all prime numbers larger than the number three. I do not know if this
always holds true, so a computer program would be needed to extensively
test this equation or somehow use logic tools to prove or disprove it.
For example: 101 + 103 = 204 and 204 is between 199 and 211
so this formula is not always true,
205 is the midpoint between 199 and 211.
So maybe we should just say that this often works though not always.
We could test a modified version of the formula such as:
primeA + primeB = either primeN +/- 1,
or else
primeA + primeB = a midpoint +/- 1 such that the midpoint is between two
sequential or two non-sequential prime numbers.
If that is true, is it only true for sequential prime number midpoints
offset by plus or minus one, or is it only true for non-sequential prime
numbers' midpoints offset by plus or minus one? Or both?
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8/7/2010 Justin Coslor
Natural Numbers (revise and coalate with other observations)
Look at the sum of two sequential large prime numbers. They always equal
an even number
because an odd number plus an odd number equals an even number. Prime
numbers larger than 2 are always odd. Yet some prime number neighborhood
midpoints are even and some are odd. So therefore not every prime number
neighborhood midpoint is the sum of two prime numbers.
The sum of any two odd numbers always equals an even number.
The sum of any even number plus any odd number always equals an odd
number.
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8/8/2010 Justin Coslor
The sum of any two or more even numbers is always an even number.
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