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Old 2013-02-08, 12:46   #1
jasong
 
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Default Prime pattern thoughts

First, I want to apologize for not knowing the proper term for the concept, but...

Maybe the reason we haven't found a pattern for prime numbers is because of the very way they're generated. A prime is a number only divisible by 1 and itself. So, by it's very definition, it's resistant to adhering to a pattern.

If I'm not mistaken, there's a mathematical concept that describes a function where you basically take a stream of numbers(or any symbol) and continue to write numbers with the main rule being you write them so that they can't be thought of as matching a pattern with the previous numbers.

So, I might start with 1, then write a 2, then write a 4 so that they're not consecutive, then write a 5 so it's not doubling of the prevous term, then write a 6 so that we're not skipping every third term, and so on.

So, maybe instead of a pattern like we normally think of it, maybe the pattern is somehow connected to the concept that I just described, but can't name.

Last fiddled with by jasong on 2013-02-08 at 12:47
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Old 2013-02-08, 13:05   #2
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Quote:
Originally Posted by jasong View Post
First, I want to apologize for not knowing the proper term for the concept, but...

Maybe the reason we haven't found a pattern for prime numbers is because of the very way they're generated. A prime is a number only divisible by 1 and itself. So, by it's very definition, it's resistant to adhering to a pattern.

If I'm not mistaken, there's a mathematical concept that describes a function where you basically take a stream of numbers(or any symbol) and continue to write numbers with the main rule being you write them so that they can't be thought of as matching a pattern with the previous numbers.

So, I might start with 1, then write a 2, then write a 4 so that they're not consecutive, then write a 5 so it's not doubling of the prevous term, then write a 6 so that we're not skipping every third term, and so on.

So, maybe instead of a pattern like we normally think of it, maybe the pattern is somehow connected to the concept that I just described, but can't name.
on kid shows someone named that type of thing a no pattern pattern.
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Old 2013-02-08, 18:09   #3
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chaos pattern?
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Old 2013-02-08, 18:45   #4
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the primes>3 are a subset of the numbers with gaps 0,2,4 mod 6 such that any one gap doesn't divide by a number already on the list , probably no ? okay maybe slightly off.

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Old 2013-02-09, 02:41   #5
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A series of numbers where the next element is chosen to not form a pattern would not look like the primes because of the twins. Am I missing something?

Last fiddled with by Flatlander on 2013-02-09 at 02:42
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Old 2013-02-10, 03:07   #6
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Originally Posted by Flatlander View Post
A series of numbers where the next element is chosen to not form a pattern would not look like the primes because of the twins. Am I missing something?
Yes, that's true. I guess it's a matter of figuring out what types of patterns to try to suppress.

If this is the the, I mean.

Last fiddled with by jasong on 2013-02-10 at 03:07
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Old 2013-02-10, 04:39   #7
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Quote:
Originally Posted by jasong View Post
Maybe the reason we haven't found a pattern for prime numbers
I'm sorry, this is a pet peeve of mine.

We've discovered hundreds, probably thousands, of patterns in the primes. Ulam spirals, Dirichlet's theorem, Wilson's theorem, the Erdős-Kac theorem, Maier's theorem, ... the list goes on. There are surely over a hundred formulas for the primes, depending on what you count: Guy's Unsolved Problems in Number Theory devotes a whole section to it, both of Ribenboim's books on primes discuss this at length, and I've seen dozens of research papers on the topic. Wikipedia and MathWorld both have long articles (which are yet rather incomplete compared to the vast published total).

How can anyone possibly question that we've discovered patterns in the primes?
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Old 2013-02-10, 15:12   #8
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http://mathworld.wolfram.com/PrimeAr...ogression.html

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It had long been conjectured that there exist arbitrarily long sequences of primes in arithmetic progression (Guy 1994)......
.
.
Thanks to new work by Ben Green and Terence Tao, the conjecture seems to finally have been settled in the positive. In a recently published in preprint, Green and Tao (2004) use an important result known as Szemerédi's theorem in combination with recent work by Goldston and Yildirim, a clever "transference principle," and 48 pages of dense and technical mathematics, to apparently establish the fundamental theorem that the prime numbers do contain arithmetic progressions of length for all (Weisstein 2004). The proof, however, is nonconstructive.
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Old 2013-02-10, 20:22   #9
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Quote:
Originally Posted by Eccl.1:15
That which is crooked can't be made straight; and that which is lacking can't be counted.
This goes for the Bible thread as well.
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Old 2013-02-11, 02:06   #10
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Ecclesiastes must've had bad arthritis (too much stiffness of the joints) or erectile dysfunction (too little), it seems.

Reminds me of the one about the old bible-belt couple sitting in their rocking chairs out on their porch, listening to the preacher on the radio. Preacher says "Now I want all of my listeners to place a hand over that part of their body which is AFFLICTED, yeah-ess, and pray with me and be HEALED, yeah-ess!" The old woman places her right hand over her heart and says "please help me heal this broken heart of mine, lawdy!" When she sees her old husband place his right hand over his crotch, she snaps "Honey, preacher man said heal the sick, not raise the dead!"
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Old 2013-02-11, 03:11   #11
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Quote:
Originally Posted by ewmayer View Post
Ecclesiastes must've had bad arthritis (too much stiffness of the joints) or erectile dysfunction (too little), it seems.

Reminds me of the one about the old bible-belt couple sitting in their rocking chairs out on their porch, listening to the preacher on the radio. Preacher says "Now I want all of my listeners to place a hand over that part of their body which is AFFLICTED, yeah-ess, and pray with me and be HEALED, yeah-ess!" The old woman places her right hand over her heart and says "please help me heal this broken heart of mine, lawdy!" When she sees her old husband place his right hand over his crotch, she snaps "Honey, preacher man said heal the sick, not raise the dead!"
THE TRUMPET SHALT SOUND
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