## prime number patterns | |

Anonymous Coward User ID: 300884 Sweden 04/24/2012 05:48 AM Report Abusive Post Report Copyright Violation | Many lives have been wasted in pursuit of the elusive prime number pattern, don't add yours to the pile. The prime number pattern is elusive, because such a pattern doesn't exist! It's very easy to find what looks like a beginning of a pattern. But any such beginning of a pattern you find soon breaks down when you check it further. Then you start looking for a pattern for when your first pattern holds and when it doesn't hold, and lo and behold, you easily find a pattern in the pattern-breaking! And then that pattern breaks too... *** The real secret is THERE IS NO PATTERN! *** You may be able to realize this intuitively, by thinking about how prime numbers are defined. A prime number is a number that can NOT be divided. Note the negation inherent to the definition. Prime numbers aren't defined as having some quality, they're defined as lacking it. It's the non-prime numbers that have a positive definition. Now, non-prime numbers follow very simple patterns. It's easy to generate an infinite amount of non-prime number: just multiply with an integer other than 1! Prime numbers are the numbers left over when you remove numbers composed by an a INFINITE number of such simple patterns. Prime numbers are thus the HOLES left after an infinite number of simple patterns. And that's why they don't have a simple pattern of their own: You can't compress an infinite number of simple patterns into a single simple pattern! |

Anonymous Coward User ID: 11171736 United Kingdom 04/24/2012 06:06 AM Report Abusive Post Report Copyright Violation | Dear OP, follow your intuituion, and your passions. Prime numbers are fascinating. The primes that you speak of sandwiching a non-prime are twin primes see [link to en.wikipedia.org] give us some examples of a particular pattern you have noticed and I'll see if I can tell you some more. |

Anonymous Coward User ID: 11171736 United Kingdom 04/27/2012 12:30 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 10830710 Canada 04/27/2012 12:41 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward (OP)User ID: 13669854 Korea, Republic of 04/27/2012 12:43 PM Report Abusive Post Report Copyright Violation | Dear OP, follow your intuituion, and your passions. Prime numbers are fascinating. Quoting: The primes that you speak of sandwiching a non-prime are twin primes see [link to en.wikipedia.org] give us some examples of a particular pattern you have noticed and I'll see if I can tell you some more. Anonymous Coward 11171736 thanks for the info and the support. can you re-read my op and tell me more of your thoughts? sadly I haven't progressed any further from my initial observation. sigh. |

Anonymous Coward (OP)User ID: 13669854 Korea, Republic of 04/27/2012 12:45 PM Report Abusive Post Report Copyright Violation | Many lives have been wasted in pursuit of the elusive prime number pattern, don't add yours to the pile. The prime number pattern is elusive, because such a pattern doesn't exist! Quoting: It's very easy to find what looks like a beginning of a pattern. But any such beginning of a pattern you find soon breaks down when you check it further. Then you start looking for a pattern for when your first pattern holds and when it doesn't hold, and lo and behold, you easily find a pattern in the pattern-breaking! And then that pattern breaks too... *** The real secret is THERE IS NO PATTERN! *** You may be able to realize this intuitively, by thinking about how prime numbers are defined. A prime number is a number that can NOT be divided. Note the negation inherent to the definition. Prime numbers aren't defined as having some quality, they're defined as lacking it. It's the non-prime numbers that have a positive definition. Now, non-prime numbers follow very simple patterns. It's easy to generate an infinite amount of non-prime number: just multiply with an integer other than 1! Prime numbers are the numbers left over when you remove numbers composed by an a INFINITE number of such simple patterns. Prime numbers are thus the HOLES left after an infinite number of simple patterns. And that's why they don't have a simple pattern of their own: You can't compress an infinite number of simple patterns into a single simple pattern! Anonymous Coward 300884 I understand what you're saying, but the devil inside me (or whatever that pos is in thar lol) says that there is a pattern. just because we don't know it, doesn't mean it doesn't exist. not a counter-argument to your words, just my own opinion, as ill eloquent as it may be. :) |

Anonymous Coward User ID: 15122892 United States 04/27/2012 12:53 PM Report Abusive Post Report Copyright Violation | First, big disclaimer, I'm not technically proficient in numbers any longer. it's been a long time for me to do math of any kind. But I noticed a post on here the other day that got me just to look at the problem for the first time for me. I know there are some serious math whizes on this site, so hope I can follow. Quoting: Honestly I don't know if some of the initial patterns in primes have already been talked about before, doing some research it's hard for me to understand the mathematical jargon. In my the simplest basic layman's terms, which is the only thing I can use in my case, when I look at the spacing between primes, lots of 3's, 5's, 7's, 9's, 11's and 13's. This has got to be a pattern of some kind! Now I've only looked at numbers up to 400, so I should probably do to at least 1,000. Maybe soon. But still another pattern that's coming up instantly is two prime numbers sandwiching a non-prime. Like 5 6 7. 5 and 7 of course being prime. And when you look at those double spaced primes, they occur with some regularity around the 10 count. like 239 240 241 for example. And when it sandwiches a perfect ten, the spacing til the next one seems to very regularly be a multiple of 30. And when the sandwich doesn't exactly land on the 10, it's always a step back (17 18 19) or one forward (41 42 43). When it's forward, their occurrences are also in multiples of 30 from the last, and when back, also in multiples of 30. Arrgh! Still the trick is trying to figure out the precise pattern, which I can't. And then the troublesome lone single primes, which don't have a real discernable pattern thus far. I can see now why no one's been able to predict thus far! I hope what I've said can be discerned and hopefully someone can tell me if I've given any thing new or not to the puzzle. Anonymous Coward 13669854 What you want to study, in what you call "spacing" between the primes is know as the prime gap: [link to en.wikipedia.org] Also, a key concept is the Prime Counting function, which tells the number of primes below a given number (there is no explicit formula for this, however): [link to en.wikipedia.org] The thing where you describe "two prime numbers sandwiching a non-prime." is known as the twin prime conjecture - that is, are there infintely many primes that are separated by one composite (non-prime). [link to en.wikipedia.org] If you would like to devote further study to this, I would suggest starting with the study of modular arithmetic and the fundamental theorem of arithmetic. Get a copy of G.H. Hardy and E. M. Wright's "An Introduction to the Theory of Numbers" it's pretty approachable and has proofs (and it's a good source to cite if you decide to write anything). Another (ok) text is "Number Theory By Inquiry", but it doesn't have alot of help for the exercises or fully detailed explaination of a lot of stuff - thats ok, it makes good companion for the Hardy and Wright text. |

Anonymous Coward User ID: 11171736 United Kingdom 04/27/2012 12:55 PM Report Abusive Post Report Copyright Violation | Prime numbers are the numbers left over when you remove numbers composed by an a INFINITE number of such simple patterns. Quoting: Anonymous Coward 300884 This is incorrect Anonymous Coward 11171736 Probably TRUE, because it reads like Anonymous Coward 10830710 It is backwards thinking, the prime numbers are not the left overs, they are the beginnings. |

Anonymous Coward User ID: 11171736 United Kingdom 04/27/2012 12:58 PM Report Abusive Post Report Copyright Violation | Dear OP, follow your intuituion, and your passions. Prime numbers are fascinating. Quoting: The primes that you speak of sandwiching a non-prime are twin primes see [link to en.wikipedia.org] give us some examples of a particular pattern you have noticed and I'll see if I can tell you some more. Anonymous Coward 11171736 thanks for the info and the support. can you re-read my op and tell me more of your thoughts? sadly I haven't progressed any further from my initial observation. sigh. Anonymous Coward 13669854 Sorry OP, I've done the pattern in pattern in pattern bit myself, there are many people who have posted on the internet about prime patters. I suggest looking for deeper meaning, meditate on the nature of primes. Just an idea, but look at fibonacci sequences as a natural growth pattern for inspiration. |

Anonymous Coward (OP)User ID: 13669854 Korea, Republic of 04/27/2012 01:00 PM Report Abusive Post Report Copyright Violation | First, big disclaimer, I'm not technically proficient in numbers any longer. it's been a long time for me to do math of any kind. But I noticed a post on here the other day that got me just to look at the problem for the first time for me. I know there are some serious math whizes on this site, so hope I can follow. Quoting: Honestly I don't know if some of the initial patterns in primes have already been talked about before, doing some research it's hard for me to understand the mathematical jargon. In my the simplest basic layman's terms, which is the only thing I can use in my case, when I look at the spacing between primes, lots of 3's, 5's, 7's, 9's, 11's and 13's. This has got to be a pattern of some kind! Now I've only looked at numbers up to 400, so I should probably do to at least 1,000. Maybe soon. But still another pattern that's coming up instantly is two prime numbers sandwiching a non-prime. Like 5 6 7. 5 and 7 of course being prime. And when you look at those double spaced primes, they occur with some regularity around the 10 count. like 239 240 241 for example. And when it sandwiches a perfect ten, the spacing til the next one seems to very regularly be a multiple of 30. And when the sandwich doesn't exactly land on the 10, it's always a step back (17 18 19) or one forward (41 42 43). When it's forward, their occurrences are also in multiples of 30 from the last, and when back, also in multiples of 30. Arrgh! Still the trick is trying to figure out the precise pattern, which I can't. And then the troublesome lone single primes, which don't have a real discernable pattern thus far. I can see now why no one's been able to predict thus far! I hope what I've said can be discerned and hopefully someone can tell me if I've given any thing new or not to the puzzle. Anonymous Coward 13669854 What you want to study, in what you call "spacing" between the primes is know as the prime gap: [link to en.wikipedia.org] Also, a key concept is the Prime Counting function, which tells the number of primes below a given number (there is no explicit formula for this, however): [link to en.wikipedia.org] The thing where you describe "two prime numbers sandwiching a non-prime." is known as the twin prime conjecture - that is, are there infintely many primes that are separated by one composite (non-prime). [link to en.wikipedia.org] If you would like to devote further study to this, I would suggest starting with the study of modular arithmetic and the fundamental theorem of arithmetic. Get a copy of G.H. Hardy and E. M. Wright's "An Introduction to the Theory of Numbers" it's pretty approachable and has proofs (and it's a good source to cite if you decide to write anything). Another (ok) text is "Number Theory By Inquiry", but it doesn't have alot of help for the exercises or fully detailed explaination of a lot of stuff - thats ok, it makes good companion for the Hardy and Wright text. Anonymous Coward 15122892 thanks very much! i am tho a stubborn mule, and this is in no way to detract from my thanks to your direction. I'm of a mindset that genius arises not from studying the works of others however. I think this is a problem so easy that a child could discover it. I hope so for my sake. lol and if not, I'll check out your suggested sources. in the meantime, I'd rather keep my outlook childlike. glad to see that I've at least taken notice of what others have. I'm insanely curious if these initial patterns hold up, and for how long. maybe I'll just take a quick glance.. |

Anonymous Coward (OP)User ID: 13669854 Korea, Republic of 04/27/2012 01:04 PM Report Abusive Post Report Copyright Violation | The primes that you speak of sandwiching a non-prime are twin primes see [link to en.wikipedia.org] give us some examples of a particular pattern you have noticed and I'll see if I can tell you some more. Anonymous Coward 11171736 thanks for the info and the support. can you re-read my op and tell me more of your thoughts? sadly I haven't progressed any further from my initial observation. sigh. Anonymous Coward 13669854 Sorry OP, I've done the pattern in pattern in pattern bit myself, there are many people who have posted on the internet about prime patters. I suggest looking for deeper meaning, meditate on the nature of primes. Just an idea, but look at fibonacci sequences as a natural growth pattern for inspiration. Anonymous Coward 11171736 that's what I've tried to do, honestly. something about the pattern indicates a fibonacci spiral of sorts, but it's not so regular. as if the spiral breathes in and out. 30 degrees. can't get it out of my head. it's like a triangular spiral, even tho I don't know what the hell that means. fractals. hmmm. fractals don't seem to repeat unless looked at from a very far and then a very narrow view. but you have to admit, the twin primes, and the odd spacing, and the factor of 30 make there at least an initial semblance of a pattern, no? |

Anonymous Coward User ID: 11171736 United Kingdom 04/27/2012 01:05 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 15122892 United States 04/27/2012 01:06 PM Report Abusive Post Report Copyright Violation | Ok, a good tool for playing is OEIS (online encyclopedia of integer sequences). If you think you have some type of pattern (in anything), you can type the sequence in, and it will return mathematically relevant sequences (with information, formula, etc) that match that pattern. [link to oeis.org] |

Anonymous Coward User ID: 11171736 United Kingdom 04/27/2012 01:07 PM Report Abusive Post Report Copyright Violation | The primes that you speak of sandwiching a non-prime are twin primes see [link to en.wikipedia.org] give us some examples of a particular pattern you have noticed and I'll see if I can tell you some more. Anonymous Coward 11171736 thanks for the info and the support. can you re-read my op and tell me more of your thoughts? sadly I haven't progressed any further from my initial observation. sigh. Anonymous Coward 13669854 Sorry OP, I've done the pattern in pattern in pattern bit myself, there are many people who have posted on the internet about prime patters. I suggest looking for deeper meaning, meditate on the nature of primes. Just an idea, but look at fibonacci sequences as a natural growth pattern for inspiration. Anonymous Coward 11171736 that's what I've tried to do, honestly. something about the pattern indicates a fibonacci spiral of sorts, but it's not so regular. as if the spiral breathes in and out. 30 degrees. can't get it out of my head. it's like a triangular spiral, even tho I don't know what the hell that means. fractals. hmmm. fractals don't seem to repeat unless looked at from a very far and then a very narrow view. but you have to admit, the twin primes, and the odd spacing, and the factor of 30 make there at least an initial semblance of a pattern, no? Anonymous Coward 13669854 Male, female, 72, black, white, golden mean, cycles, birth, death. |

Anonymous Coward User ID: 11171736 United Kingdom 04/27/2012 01:08 PM Report Abusive Post Report Copyright Violation | Ok, a good tool for playing is OEIS (online encyclopedia of integer sequences). If you think you have some type of pattern (in anything), you can type the sequence in, and it will return mathematically relevant sequences (with information, formula, etc) that match that pattern. Quoting: [link to oeis.org] Anonymous Coward 15122892 yeah, that's an awesome site, some of the explanations are a little terse for my liking but that's mathematicians for you ;-) |

Anonymous Coward User ID: 11171736 United Kingdom 04/27/2012 01:16 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 15148246 United States 04/27/2012 01:16 PM Report Abusive Post Report Copyright Violation | The primes that you speak of sandwiching a non-prime are twin primes see [link to en.wikipedia.org] give us some examples of a particular pattern you have noticed and I'll see if I can tell you some more. Anonymous Coward 11171736 Encouraging mental illness is a Federal Crime. If this poor soul jumps off a bridge, you will be liable for prosecution. The penalty is $50,000, and indefinite confinement in a mental instituion of your choice. (42 USC) |

Anonymous Coward (OP)User ID: 13669854 Korea, Republic of 04/27/2012 01:20 PM Report Abusive Post Report Copyright Violation | The primes that you speak of sandwiching a non-prime are twin primes see [link to en.wikipedia.org] give us some examples of a particular pattern you have noticed and I'll see if I can tell you some more. Anonymous Coward 11171736 Encouraging mental illness is a Federal Crime. If this poor soul jumps off a bridge, you will be liable for prosecution. The penalty is $50,000, and indefinite confinement in a mental instituion of your choice. (42 USC) Anonymous Coward 15148246 oh c'mon that's not even a fair logical argument! now let me watch and learn the vids/info provided will ya? besides, there's no bridges here in korea that don't have water underneath, so good luck trying to kill me in that regards. koreans. they probably didn't even think of that fact, even tho they glass up the subway entrances to prevent suicides. |

Anonymous Coward User ID: 1418736 United States 04/27/2012 01:22 PM Report Abusive Post Report Copyright Violation | Contact Peter Plichta and his Prime Number Cross [link to www.journals.uts.edu] [link to www.plichta.de] |

Anonymous Coward (OP)User ID: 13669854 Korea, Republic of 04/27/2012 01:26 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 11171736 United Kingdom 04/27/2012 01:36 PM Report Abusive Post Report Copyright Violation | The primes that you speak of sandwiching a non-prime are twin primes see [link to en.wikipedia.org] give us some examples of a particular pattern you have noticed and I'll see if I can tell you some more. Anonymous Coward 11171736 Encouraging mental illness is a Federal Crime. If this poor soul jumps off a bridge, you will be liable for prosecution. The penalty is $50,000, and indefinite confinement in a mental instituion of your choice. (42 USC) Anonymous Coward 15148246 oh c'mon that's not even a fair logical argument! now let me watch and learn the vids/info provided will ya? besides, there's no bridges here in korea that don't have water underneath, so good luck trying to kill me in that regards. koreans. they probably didn't even think of that fact, even tho they glass up the subway entrances to prevent suicides. Anonymous Coward 13669854 Well he has a point, plenty of people have gone nuts trying to solve prime theories. I think if attempted, it should be done with wonder and awe and humility, never assuming we can solve it, but trying to get to know the primes better, see some of the magic, there is always hope. When it becomes a drag or a task we are looking at it wrongly. If we start with the sense of mystery we can always remind ourselves why we began. |

Anonymous Coward (OP)User ID: 13669854 Korea, Republic of 04/27/2012 02:40 PM Report Abusive Post Report Copyright Violation | The primes that you speak of sandwiching a non-prime are twin primes see [link to en.wikipedia.org] give us some examples of a particular pattern you have noticed and I'll see if I can tell you some more. Anonymous Coward 11171736 Encouraging mental illness is a Federal Crime. If this poor soul jumps off a bridge, you will be liable for prosecution. The penalty is $50,000, and indefinite confinement in a mental instituion of your choice. (42 USC) Anonymous Coward 15148246 oh c'mon that's not even a fair logical argument! now let me watch and learn the vids/info provided will ya? besides, there's no bridges here in korea that don't have water underneath, so good luck trying to kill me in that regards. koreans. they probably didn't even think of that fact, even tho they glass up the subway entrances to prevent suicides. Anonymous Coward 13669854 Well he has a point, plenty of people have gone nuts trying to solve prime theories. I think if attempted, it should be done with wonder and awe and humility, never assuming we can solve it, but trying to get to know the primes better, see some of the magic, there is always hope. When it becomes a drag or a task we are looking at it wrongly. If we start with the sense of mystery we can always remind ourselves why we began. Anonymous Coward 11171736 My goal. I need to go an meditate now I think. To be a bit non-humble if that's a word, I've brought to light a number of things unawares to many by just spontaneity. I'll be back lol |

psyopticsUser ID: 14240707 United States 04/27/2012 02:54 PM Report Abusive Post Report Copyright Violation | now if you want some cool divison stuff start with 1 and divide every whole number by 9....... 1/9=.111111111 2/9=.22222222 8/9-.8888888 but 9/9=1 or is it .9999999999? 10/9=1.1111111 0 is a cool number! EDIT:oh my the typo to end all typos.... 9...9 is a cool number and 0 is okay too. i think math was around for awile till 0 was used...india i think did it. has anyone seen this video before? Last Edited by psyoptics on 04/27/2012 03:22 PM a good video editor can make anyone say anything the editor wants. |

Anonymous Coward (OP)User ID: 13669854 Korea, Republic of 04/27/2012 03:05 PM Report Abusive Post Report Copyright Violation | now if you want some cool divison stuff Quoting: start with 1 and divid every whole number by 9....... 1/9=.111111111 2/9=.22222222 8/9-.8888888 but 9/9=1 or is it .9999999999? 10/9=1.1111111 0 is a cool number! has anyone seen this video before? psyoptics I think this is why I have such a love for numbers. I'm kind of sad because I grew up in a very hickville town, we didn't have enough students to have calculus, so all I had after geometry and trig and calculus2 in highschool was senior math. god how dull. but things like donald duck stay with us lol doesn't make sense in the common sense of the word to think that .99999 on into infinity is the same as 1. but it is. and then to think about a circle. so perfect, yet so unfathomable, just like the atari game. |

Anonymous Coward User ID: 15024132 Portugal 04/27/2012 04:23 PM Report Abusive Post Report Copyright Violation | Many lives have been wasted in pursuit of the elusive prime number pattern, don't add yours to the pile. The prime number pattern is elusive, because such a pattern doesn't exist! Quoting: Anonymous Coward 300884 You cannot state that. Maybe it exists but it is not accessible to us humans. The same can be said about patterns inside Pi. It's very easy to find what looks like a beginning of a pattern. But any such beginning of a pattern you find soon breaks down when you check it further. Then you start looking for a pattern for when your first pattern holds and when it doesn't hold, and lo and behold, you easily find a pattern in the pattern-breaking! Quoting: And then that pattern breaks too... *** The real secret is THERE IS NO PATTERN! *** You may be able to realize this intuitively, by thinking about how prime numbers are defined. A prime number is a number that can NOT be divided. Note the negation inherent to the definition. Prime numbers aren't defined as having some quality, they're defined as lacking it. It's the non-prime numbers that have a positive definition. Anonymous Coward 300884 You are being misled by a particular use of language. It depends on how you phrase the definition. If I say: "Let me see which numbers partake on the quality of being dividable only by themselves AND the unity" I am looking for a positive definition, not a negative one. Now, non-prime numbers follow very simple patterns. It's easy to generate an infinite amount of non-prime number: just multiply with an integer other than 1! Quoting: Prime numbers are the numbers left over when you remove numbers composed by an a INFINITE number of such simple patterns. Prime numbers are thus the HOLES left after an infinite number of simple patterns. And that's why they don't have a simple pattern of their own: You can't compress an infinite number of simple patterns into a single simple pattern! Anonymous Coward 300884 That's a way of putting it, but not the only one. Language again. As an example, you should really reflect on the notion of "floating point". The Ancients said that the gods made the integer numbers and man made the fractional ones. Why? There's only integer numbers, but since we cannot practically express the infinite we need to use a shifting, floating point in order to use the numbers in a practical way. It all depends on how we calibrate our units of measure. |

Anonymous Coward User ID: 15167986 Netherlands 04/27/2012 04:27 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 15185216 United States 04/27/2012 09:27 PM Report Abusive Post Report Copyright Violation | Hi again OP, if you like repeating decimals and prime numbers, check out how the two are related: [link to en.wikipedia.org] 1/p^2 where p is any prime other than 2 or 5, then the number of fractional decimal digits (right of point) are equal to f(p^2) where f(x) is the Carmichael function. It's somewhat related to Euler's Totient function and the prime counting function from earlier. BTW, if you don't have a calculus class and you want to learn it, why not check out the Kahn academy or download some textbooks somewhere? |

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Anonymous Coward User ID: 11171736 United Kingdom 04/29/2012 03:36 PM Report Abusive Post Report Copyright Violation | |