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Old 2012-03-06, 19:39   #1
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
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Default Prime Constellations

I have been developing a java application to find prime constellations. Constelations of length are twin primes. Constellations of length 3 have one of two patterns- [0,2,6] or [0,4,6]. More can be found on a power point presentation at -
https://sites.google.com/site/mattc1anderson/home-1

I'm hoping that some people who read this post will download the application, and search for constellations.

There is a .bat file in the src directory. Let me know if there are questions or comments.

Constellations of lenght 20 have not been found yet. You can make history and be the first.
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Old 2012-03-06, 19:44   #2
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oops the .zip didn't attach
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File Type: zip prime numbers.zip (74.4 KB, 126 views)
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Old 2012-03-06, 20:57   #3
R.D. Silverman
 
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Originally Posted by MattcAnderson View Post

Constellations of lenght 20 have not been found yet. You can make history and be the first.
And your source for this (grossly false!) information is?
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Old 2012-03-06, 22:22   #4
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Originally Posted by R.D. Silverman View Post
And your source for this (grossly false!) information is?
I looked up prime constellation can you tell me what the biggest one is the source that I can find is 24 is the first unknown.
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Old 2012-03-06, 22:33   #5
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I looked up prime constellation can you tell me what the biggest one is the source that I can find is 24 is the first unknown.
A minute of thinking about the problem should readily reveal that there isn't
a biggest one. Constructing one of arbitrary size is not difficult.

See, e.g. http://www.ieeta.pt/~tos/apc.html

Now can we end this silly discussion please?
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Old 2012-03-06, 23:48   #6
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Quote:
Originally Posted by R.D. Silverman View Post
A minute of thinking about the problem should readily reveal that there isn't
a biggest one. Constructing one of arbitrary size is not difficult.

See, e.g. http://www.ieeta.pt/~tos/apc.html

Now can we end this silly discussion please?
What you call (admissible) constellation, OP calls pattern. Therefore, I guess when OP says constellation, he's referring to actual primes fitting a (admissible) constellation.
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Old 2012-03-07, 00:46   #7
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Originally Posted by axn View Post
What you call (admissible) constellation, OP calls pattern. Therefore, I guess when OP says constellation, he's referring to actual primes fitting a (admissible) constellation.
(1) Newbies should not invent new terminology. It is not what I
call an admissible contellation that matters. It is what the mathematical
community calls it. "actual primes" is an instance of a constellation.
A constellation is a set of linear univariate POLYNOMIALS.
e.g. [x, x+2, x+6]. Specifying an actual value for x gives an instance.
Actually, under Schinzel's conjecture, the definition can be broadened
to include non-linear polynomials as well.

(2) Allow me to point out that there are 25 primes less than 100. There
are also 25 primes in [13, 113]. Each of these form "patterns". They are
two different patterns [instances of admissible constellations] in an interval
of length 100. Unfortunately, these are the only two such "patterns" that
exist. There are only finitely many instances of a constellation
of size 25 in an interval of length 100. To get infinitely many instances
of a constellation of size 25 one needs an interval larger than 100.
Offhand, I do not know exactly how big such an interval needs to be.
It would not be a hard calculation.

A. Schinzel proved this. He (and my ex) also showed that the largest
admissible constellation in an interval of length 100 that occurs i.o. has
size 23, not 25.

Now can the newbies please get off this subject until they have actually
studied it? Repeat after me: Google is my friend. Look up
"Bateman-Horn" as well.
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Old 2012-03-07, 01:10   #8
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Quote:
Originally Posted by R.D. Silverman View Post
(1) Newbies should not invent new terminology. It is not what I
call an admissible contellation that matters. It is what the mathematical
community calls it. "actual primes" is an instance of a constellation.
A constellation is a set of linear univariate POLYNOMIALS.
e.g. [x, x+2, x+6]. Specifying an actual value for x gives an instance.
Actually, under Schinzel's conjecture, the definition can be broadened
to include non-linear polynomials as well.

(2) Allow me to point out that there are 25 primes less than 100. There
are also 25 primes in [13, 113]. Each of these form "patterns". They are
two different patterns [instances of admissible constellations] in an interval
of length 100. Unfortunately, these are the only two such "patterns" that
exist. There are only finitely many instances of a constellation
of size 25 in an interval of length 100. To get infinitely many instances
of a constellation of size 25 one needs an interval larger than 100.
Offhand, I do not know exactly how big such an interval needs to be.
It would not be a hard calculation.

A. Schinzel proved this. He (and my ex) also showed that the largest
admissible constellation in an interval of length 100 that occurs i.o. has
size 23, not 25.

Now can the newbies please get off this subject until they have actually
studied it? Repeat after me: Google is my friend. Look up
"Bateman-Horn" as well.
Slight correction. Because the 25 primes in [13,113] can only happen
finitely often, they do not form an admissible constellation
by definition.
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Old 2012-03-07, 06:22   #9
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Quote:
Originally Posted by R.D. Silverman View Post
A minute of thinking about the problem should readily reveal that there isn't a biggest one.
Once you see a newbie post with imprecise or just-plain-wrong terminology, a moment of reflection should clue you in to its being a situation you should leave to others to handle. You've repeatedly demonstrated your ineptitude in handling imprecisely-worded newbie posts.

Suggested guideline: whenever you see that a new thread, by someone who's not a forum veteran, contains inexact terminology, skip it and go somewhere else, without posting any reply. Let some other forum member(s) take care of determining the meaning and straightening out the newbie's terminology. Later, when you come back and see that the terminology has been straightened out, contribute in one of the many ways in which you really do have superior competency.

If a known forum veteran posts inexact terminology, then feel free to post a correction right away.
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Old 2012-03-07, 11:04   #10
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Quote:
Originally Posted by cheesehead View Post
Once you see a newbie post with imprecise or just-plain-wrong terminology, a moment of reflection should clue you in to its being a situation you should leave to others to handle. You've repeatedly demonstrated your ineptitude in handling imprecisely-worded newbie posts.
On the contrary, I said exactly what needed to be said.
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Old 2012-03-07, 14:08   #11
xilman
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Quote:
Originally Posted by R.D. Silverman View Post
On the contrary, I said exactly what needed to be said.
You might very well think that; I couldn't possibly comment.
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