What formulas to determine patterns for Prime Numbers?

" ..The prime numbers grow like weeds among the natural numbers..." , so, if you just hoped for a nice polynomial formula that produces all primes you are out of luck.

The Sieve of Eratosthenes, (see image at this link),......

http://www.onlinemathlearning.com/image-files/siev...

....strikes out composite numbers and leaves the primes standing and online you can obtain huge (pointless) lists of primes.

The distribution of primes:

Although the 1/ln x and other closer formulae, (described in the previous post and online), are interesting they are not exact which is frustrating; and of course you may already know more than you wanted to about the Riemann Zeta Function.

I found this page readable and liked the quantum physics analogy.

http://www.timetoeternity.com/time_space_light/pri...

However, if all that was much too heavy, it might amuse you to play with values of x substituted into x^2 + x + 17, which generates some prime numbers for all integer values of x from 0 through 15.

Another like that is x^2 + x + 41, which yields an unbroken string of 40 primes, starting at x = 0.

Regards - Ian

there is not any longer a progression in determining a best wide type. starting up with 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 40-one, 40 3, 40 seven, and fifty 3, it variety of feels variety of peculiar for the progression to bypass as +a million, +2, +2, +4. +2, +4, +2, +4, +6, +2, +6, +4, +2, and +4. there is an uncertain progression, even if it can't particularly be conjured. there is not any longer a optimum best wide type yet. It hasn't been got here upon, yet i imagine that there is considering each and each and every of the large numbers will be divisible to different smaller composite numbers.

I dont find the paper convincing.

He starts out by referencing ancient scripture, for one. And tries to explain that concepts are different in different cultures.

He also references Oxfords English dictionary, as opposed to a mathematical dictionary for a more rigorous mathematical meaning.

For some reason he is obsessed with subtracting the cardinalities of two infinite sets, which has no practical application in the math. The math requires that the associated terms between two sets are subtracted, producing a third set. But he wants the third set to have a cardinality of other than that of the two previous sets. I dont understand where he is going with that. If set two is generated by multiplying set one by a non-zero constant, then sets one and two have the same cardinality. The difference in corresponding elements of these sets will generate a set of equal cardinality.

I dont think he grasps what infinity means. At one point he makes on simple fallacy; the one common to students who think 0.99999.... is not 1. Its the similar line of reasoning he uses to justify a difference in cardinality.

He even says "infinity boundary", whatever that means, starts after "finite boundary", but before some imagined "holiness boundary"

You can tell by his use of English, never mind his persistence on referencing mysticism, that he does not think in a very coherent manner.

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One does not have to reference the RH specifically to show fallacy in an argument. You might want to research basic reasoning skills and logic.

It doesnt matter what his subjective interpretation of infinity is. What matters in a mathematical context are the established definitions used amongst mathematicians.

The fact that you would down thumb me for pointing out how wrong he is... (and oddly enough I seem to be the only person to have read the article)... proves to me that you are not being unbiased or fair. You have no interest in the truth, do you?

Perhaps you are the one who wrote the article in the first place. After all, how do you find such an obscure paper, and why would you utilize it when so many credible mathematicians discount it?

You are correct about the expected importance of Riemann's Hypothesis, but it is for very good reasons that is known as the Graveyard of Mathemeticians - we will probably never know just how many Mathematicians have gone insane trying to prove it. Riemann himself suffered a nervous breakdown, and the American John Nash went insane. The poor man starved to death because he was convinced that everybody was trying to poison him. It has often been said there is a very fine dividing line between genius & insanity, and nowhere is that illustrated better than in the field of Mathematics. Goldbach's Cojecture is another one that has claimed its share of victims.

Yes, there is a formula to predict the number of primes in the first n natural numbers. But I can't remember it...it might be: (n) / (ln n). So, in the first 1000000 natural numbers, it is predicted that there are 1000000/ln 1000000 = 72382 primes. And yes, you're right...it is an open question.

I have discovered recently 4 Matrix equations which lead to the Matrix Primes reside.

I have also proven, as a consequence, the Twin Primes and Golbach's conjectures.

Open the links in the Primes revisited section of https://mit.academia.edu/ConstantineAdraktasPrimeN...

Constantine Adraktas

Constantine.Adraktas@MIT-Partners.eu

There are formulas which approximate the number of prime numbers from 1 to n.

Everything you could want to know about prime numbers is here.

http://primes.utm.edu/

The formulas I'm talking about are here:

http://primes.utm.edu/howmany.shtml

This person keeps changing his name and popping up somewhere with the same unfounded claims. It is all based on the idea that "numbers" such as ...9999999123 are natural numbers. Sort of a transferrence of the p-adic number system to the p-eano number system. It's all nonsense. Please don't argue with him. It will do you no good.