### New pattern found in prime numbers

According to the article:

At first the article title excited me, but this new "discovery" doesn't mean much to me.

There is a pattern to the primes, and I know what it is, but I don't know how to express it in an equation, so I've never been able to do much with my brilliant knowledge. (And it's non-recursive... a recursive function is cheating!)

In a recent study, Bartolo Luque and Lucas Lacasa of the Universidad PolitĂ©cnica de Madrid in Spain have discovered a new pattern in primes that has surprisingly gone unnoticed until now. They found that the distribution of the leading digit in the prime number sequence can be described by a generalization of Benfordâ€™s law.

At first the article title excited me, but this new "discovery" doesn't mean much to me.

There is a pattern to the primes, and I know what it is, but I don't know how to express it in an equation, so I've never been able to do much with my brilliant knowledge. (And it's non-recursive... a recursive function is cheating!)

## 6 Comments:

whilst I understand recursion, I am not sure how you can say there is a pattern in the primes, which all appear to be dependent on what proceeded it could somehow exist without some type of recursive process ?

By Tone, at 1:21 AM

I know, that's the beauty of it... the numbers really don't depend on what preceded them. Similarly with the Fibonacci sequence... the pattern can be easily expressed and understood with recursion, but it can also be expressed by a function without recursion.

But I don't want to give it away until I can figure out how to express it as an equation... so for now my comment us just a useless unverifiable proclamation. Definitely possible though.

By Sean Hannifin, at 3:38 AM

I understand where you are coming from. I too have "wasted" many hours obsessing about primes and do not know how to express it in the current mathematical lingo.

Perhaps we each hold an idea that will progress the understanding of primes if we work out how to express it - but maybe not.

Are you referring to a particular type of prime such as mersenne primes.

On the issue of recursion, your idea may be novel but I can write an algorithm that is not recursive that does the same thing as a recursive process. I expect that your idea that what you have found dose not "depend on what preceded them" is your advance, not the avoidance of recursion.

TonyM

By Tone, at 4:18 AM

I'm referring to all primes (though I'm not sure about the number 1, though by most definitions its considered to not be prime).

As for recursion, I don't mean it simply doesn't need recursion, but that it doesn't have to go through all the other prime numbers to find the nth prime, just as to find the nth square number, you simply calculate n^2 without needing to go through all the square numbers. But the pattern of square numbers is easy.

By Sean Hannifin, at 5:15 AM

I thought that was what you meant. Sounds good to my mind. I hope you can find a mathematical way to express it. My ideas are similar to those found at http://www.ma.utexas.edu/mp_arc/c/06/06-314.pdf

But I can only scan it not grasp all of the maths.

What ever the outcome our studies teach us more about the numbers than any formal lesson don't they.

By Tone, at 5:21 AM

Interesting article! I can't understand all the math there either, but I've definitely noticed the "symmetries" and I think that's important ... I also think there's something helpful with the Reimann Hypothesis, which I used to semi-understand a few years ago when I was really interested in this stuff.

Yes, personal exploration fueled by personal interest is much more powerful than formal lessons! Actually, in other posts in my blogs, I sometimes rant about how much I loathe formal education, but I guess that's a different subject.

By Sean Hannifin, at 1:25 PM

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