Tesla TOE Member Quest Prime Numbers

[theunify]

Tesla

07-16-2006 04:50 PM

Pattern in primes
I have found a SIMPLE mathmatical pattern in primes! It is a laughably elementary formula showing an obvious pattern. I quit laughing when I started hitting big numbers though. I know a little java but not quite enough to make a program to do it all for me. Help if your interested. What've you got to loose?

Need some motivation? Well it's one of the millenium problems worth one million dollars for the answer.

Don't hesitate to reply, "lol". Sticks and stones.

Thanks.

Tesla

07-16-2006 06:32 PM

Re: Pattern in primes
Sure thing! Visit this link, http://www.claymath.org/millennium/, and get back to me.

Thanks.



Tesla

07-16-2006 08:27 PM

Re: Pattern in primes
Here we go:

3(x)-(1,2)

Beautiful! But hardly refined as you will see.

Here are the rules:

If the x you are plugging in is odd then subtract (the even) 2

If the x you are plugging in is even then subtract (the odd) 1

Now plug 1 in for x and you get 1, the first prime (I know that 1 is'nt accepted as a prime and 2 is but this will change that)

Now plug in 2 for x (remember 2 is even so you subtract 1) and you get 5, the third prime (where'd 3 go? It does't show because it's fixed in the equation itself, I just call it an understood prime)

Now plug 3 in for x and you get 7.
Now 4 (=11).
Now 5 (=13).
Now 6 (=17).
-----------------------------------
9 is the first number (in a list of many) you'll plug in and not get a prime out.

Here's why (rule number two):

You can use this formula to produce sequencial primes forever but their are hangnails, here's how to clip them...

The first NP (non-prime) you'll get is 25 (3(9)-2)
25 is 5*5

The second NP you'll get is 35 (3(12)-1)
35 is 5*7

Another is 55 (5*11)

Another is 65 (5*13)

Notice the numbers italicized are the numbers produced by the formula (going in ascending order from 5); so the next hangnail will be 5*17, then 5*19, then *23, then *25 (it's not prime but still on the list: 3(9)-2=25), and so on...

Now go to 7 (next on the list)
7*7 is 49 an NP (3(17)-2=49)

7*11 is 77 (3(26)-1=77)

7*13 is 91 (3(31)-2=91)

Now 11
11*11 is 121 (3(41)-2=121)
11*13
11*17
11*19, 11*23, 11*25, 11*29, and so on and so forth...

But don't really clip the hangnails; just flag them because you will need them in order to find others.
-----------------------------------
It's a pattern, it's in order, and it's raw and unrefined. It is elementary, yet infallable. I just need to figure out how to use it with the Riemann Hypothesis (if possible). In any case it's still a pattern! Chew on that!

You might want to read it again. It gets to be a headache and thats why I want to make a java program of it all. Anyhow, tell me what you think.

Thanks.

[theunify]

Post deleted.

[Robert "Bob" Shriner]

Yes you are on the right track. As I posted here about two years ago you will find that if you build an array of the numbers generated as 6N (+1,-1) you have a set 1,5,7,11,13,17,19,23,25,29 repeating in the first digit in sets of 30x. The products of this array constitute all products of Primes and Prime products with the first being 25 as 5x5. If you project the Squares of the P & PP you will split the array to (an upper and lower section) this is a duplicate as 5*7 and 7*5. Using the upper section and numbers > than the square you will have a list of PP including PP harmonics 5*7*11 and 35*11 and 5*77. If you Look at the array and extend the products of 5, as an example out till it achieves its highest product less than C (the prime product) (Riemann Hyp) you will then see that this projection is the exact number of products less than C for each value in the array. For simplicity counting the number of prime products in this region above the Square and less than C you will be able to see and count the number of values less than C. If you subtract the number of PP from the positional number of C then you have the exact number of Primes less than C. Hmmmm
In addition you will see that a curved Line is developed in the array as each value is projected out greater than the the square and =<C. This is a line that separates the Greater than C and Less than C values in the array. The detail that is now realized is that if C is a PP then it will fall on this line and if it is not it is a Prime. If each value in the sequence is designated as A then you have the product sequence 6NA,-A,+A for each value A. As you go farther into this you will find that (as an example) the value 5 is position two and (5*5)= 25 is position 9 and (5*7)=35 is position 12 and farther in a series of product positions for 2 step (+7,+3) and for value 7 position 3 steps as (+9,+5). You are on the right track as each position and each value can be derived from the other but be care full as this requires two formula for each condition position to value or value to position.
What I found unique is that 6N(-1,+1) for whole real numbers and N =0 step 1 is a list that when multiplied against itself (6N(-1,+1))(6N(-1,+1))= a list of all PP and the removal of these values from list 6N(-1,+1) = 100% Primes equal to and greater than 5 in sequence and without exception. 6N sequence removes all products of 2 and 3 and 2*3 from the list as an additional filter from the sieve of Eratosthenes. I believe that the understanding generated here is great. I am not a mathematician, I am good at finding patterns overall. I do not know how Riemanns' Hypothisis is generated but this array is specific to the same answer. All patterns that I have found in value exists in positions and each can be converted to the other. I believe that this is a derivable pattern to the Prime but lack the computer skills to mount a viable proposal. Sets of products are formed by each value A in sets 30x and positional sets of 10x. Every pattern that I have found using these patterns are consistent and applicable to each value.
I have enjoyed this search for several years and still find more each time I seek that formula to factor a Prime Product. (succeeded 126 digit pp in two weeks on a single pc but still numbers crunching and I believe that these patterns hold the key to factorization of large, and small, Prime Products.)
Work in Progress.

[Cubola Zaruka]

This method is the Eratosthenes Seive, which has been known for a long time. The only difference is in the initial 3(x)-(1,2), which is a more complex way of describing the process of striking out multiples of 2 and 3.