Hi, what I did to try to find prime numbers was this (in a computer program)(adsbygoogle = window.adsbygoogle || []).push({});

Starting from 2, I set off a sine wave that has an amplitude=0 for every even number and an amplitude=1 for every odd number. What we are looking for, then, are the portions of the sine wave where the derivative (slope) is zero (ie, a local maximum).

It is easy to see that this will occur precisely at the integer, 3. Then, I repeat the process, such that, starting at 3, I set off a 2/3 probability wave, meaning that it on touches down on every third number.

Here's where things start to get interesting. According to the 2-wave, the next maximum is precisely at 5, and according to the 3-wave, it is precisely at 4.5 (directly in between 3 and 6).

So what I did to find the next maximum was to sum the [absolute values of the] amplitudes of the two waves into a composite waveform, and the next maximum was somewhere around 4.85 (The level of granualarity between integers was .01).

At this point, I realized that I needed to do some filtering, such that maximums that were within 20% of the nearest integer would qualify as being "good hits" (ie prime numbers) while the maximums outside of this range could be discarded. Actually, it seemed that anywhere between 15-20% would suffice because, regardless of the value, there would be the same total of: non-primes that were taken as being "good" and primes that were "no good". But by in large, this process worked rather well in the domain from 2-100.

Here is the data:

6 primes were outside of the 20% boundary, with the worst being 29% away.

12 non-primes were accepted, that should not have been.

About 40 non-primes were successfully filtered out.

But the really interesting thing is that many of the values that I got were strongly correlated to the halves of the imaginary values of the Riemann zeros. ie 1/2 of the first zeta zero is about 7.07 vs one of my maximums is 7.19.

And here was the most interesting string of correlated values (the first is mine):

81.53-81.52

82.71-82.77

(skipped two of his values...)

84.96-84.96

86.68-86.71

87.39-87.38

All in all, I did get roughly the same rate of maximums as there were [halved] zeta zeros, and there seems to average a difference of around 0.5 between his number and my closest number.

Also, I've written a program that plots the composite probability function, so that I see better now how to tell if a maximum within the 20% range should be treated as a "good hit" or not... it has to do with the level of the next maximum being lower than the level of the previous "good hit". It looks like a bearish stock trend, that, when it reverses, the next maximum that is close to the same height as the previous one will most likely be a prime number.

My question is whether any of you think that I might have hit upon anything interesting, or whether this is a way of approaching the question of the "pattern of the primes" that has already been done.

I haven't been able to find any references to anything like this, and I know that my method is not totally unrelated to Riemann's, because he starts his paper with the Euler product, which is just the multiplication of:

1/(1-1/p^s), where p is all prime numbers.

This equation can be written as:

1/((p^s)-1)/p^s = p^s/(p^s)-1

Well, my probability waves are simply the inverse of this, ie (p^s)-1/p^s, where s=1.

In other words, when each new wave is generated, you get an ever diminishing probability:

1/2 * 2/3 * 4/5 * 6/7 * 10/11 * 12/13 ...

If anyone is interested, I can share my code with you. (The graphical stuff uses the X11 Linux library)

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# Interesting method for prime discovery?

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