mersenneforum.org Prime pattern thoughts
 Register FAQ Search Today's Posts Mark Forums Read

 2013-02-08, 12:46 #1 jasong     "Jason Goatcher" Mar 2005 1101101100112 Posts 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
2013-02-08, 13:05   #2
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by jasong 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.

 2013-02-08, 18:09 #3 firejuggler     Apr 2010 Over the rainbow 1001111010112 Posts chaos pattern?
 2013-02-08, 18:45 #4 science_man_88     "Forget I exist" Jul 2009 Dumbassville 26·131 Posts 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. Last fiddled with by science_man_88 on 2013-02-08 at 18:46
 2013-02-09, 02:41 #5 Flatlander I quite division it     "Chris" Feb 2005 England 1000000111012 Posts 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
2013-02-10, 03:07   #6
jasong

"Jason Goatcher"
Mar 2005

3·7·167 Posts

Quote:
 Originally Posted by Flatlander 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

2013-02-10, 04:39   #7
CRGreathouse

Aug 2006

32×5×7×19 Posts

Quote:
 Originally Posted by jasong 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?

2013-02-10, 15:12   #8
ATH
Einyen

Dec 2003
Denmark

307810 Posts

http://mathworld.wolfram.com/PrimeAr...ogression.html

Quote:
 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.

2013-02-10, 20:22   #9
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

9,391 Posts

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.

 2013-02-11, 02:06 #10 ewmayer ∂2ω=0     Sep 2002 República de California 2×5,813 Posts 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!"
2013-02-11, 03:11   #11
davieddy

"Lucan"
Dec 2006
England

2·3·13·83 Posts

Quote:
 Originally Posted by ewmayer 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

 Similar Threads Thread Thread Starter Forum Replies Last Post WraithX Other Mathematical Topics 17 2017-01-10 19:57 matthewsx7 Miscellaneous Math 21 2016-06-25 08:30 ProximaCentauri Miscellaneous Math 22 2014-12-05 13:07 TrdH Miscellaneous Math 41 2014-03-17 00:35 davar55 Miscellaneous Math 36 2011-01-19 15:21

All times are UTC. The time now is 20:20.

Tue Apr 20 20:20:04 UTC 2021 up 12 days, 15 hrs, 1 user, load averages: 3.50, 3.33, 3.22