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#91
May3005, 04:07 AM

P: 408

Take this:http://homepage.ntlworld.com/paul.va...ME%20GRIDS.htm I discovered that the 'Erosieve' is not anatural representation of the numbers used, if one diagonalize's the cells into a certain progressive angle, then certain patterns arise. I did not know at the time that this pattern is actually pertaining to:http://eureka.ya.com/angelgalicia30/Primesbehaviour.htm which is quite an amazing site! One can see that Prime numbers behave in a specific way?..if one uses the 'rectangle Sieve' for the first one hundered primes, there is NO concerning pattern that emerges. But if one Diagonalize's the sieve boxes, then one see's the Pattern is Emergent! What is the significance?..it happens to be connected to Fractals and Prime Number distribution of real numbers, and my lack of Mathematical skills gave me a false sense of achievement ..the process was allready in existence, with maybe a slight of hand! 


#92
May3005, 07:03 AM

Sci Advisor
HW Helper
P: 1,995

Same thing. In a basic Eratosthenes of size N you'll store your information in a string of N bits, where the nth bit is 1 if n is prime, 0 if it's composite. You start with a string of all 1's, 111111.... First stage you remove 1: 011111... Next stage multiples of 2:0110101010... then multiples of 3:01101010001.. And so on. Presieving by 2 and 3 is not only to save time but space. We need only consider numbers congruent to 1 or 5 mod 6, so this is the sequence we store. We need only about N/3 bits, the first bit represents 1, the next 5, the next 7, the next 11, then 13, and so on. Each pair of bits is one of your rows, so I'm going to seperate them with commas. First stage we knock off 1: 01,11,11,11,11,11,... Next stage we knock off multiples of 5, this isn't as straightforward due to how our string is indexed, but we can easily see that we need to jump ahead 4 pairs and remove the first in the pair (this is 25) then we jump ahead one pair and remove the second (35) to get: 01,11,11,11,01,10,...And we continue jumping 4 pairs, 1 pair, 4 pairs, 1 pair crossing off as we go. Replace pair with line and this is what you're describing. I described in an earlier post how you'll know how many pairs (used your line terminology) to jump based on the k and the 1 or 5 in your primes representation as p=6k+1 or p=6k+5. Here k is just indexing the pair (or line) you're in (starting at 0) and 1 or 5 is whether you are 1st or 2nd in the pair. A nice thing about Euclid's proof is that it's somewhat constructive and you can phrase in such a way to avoid the troublesome "infinite". If you take *any* finite list of primes then it not only guarantees there is a prime not on your list but also gives a multiple of this new prime, so you could find it with a little factoring. If you start with 3 and 5 it gives N=3*5+1=16, which though not prime has a the prime divisor 2, not on our list. We now take 2,3,5 and make N=2*3*5+1=31, another prime not on our list. So, when you've gotten to the point where you think you have all the primes, find the corresponding N and then what? What in your "reality" goes wrong? Did you just find a number with no prime factors? (do you think that's possible?) 


#93
May3005, 11:20 AM

P: 104

I do not try to undermine math, math is fine as it is. I was just answering a question, and bumped into the limitations. You may think the limitations are inside of me (and you may be right), I think the limitation exist in math (in that it is abstract only, despite its many realistic applications). The thread divulged into a question about the infinite, which does not belong in this thread. My famous last words: I think the infinite in math is a mirror's mirror's image that is being given value. The infinite image truly exists — we need not argue about that — but is it still reflective of reality? Thanks again. 


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