Good morning all,

I seek to present an approach, to find the distribution of prime numbers in the set of integers.

I'm trying to find out if we've already thought about this approach and your criticism of this approach.

Let the series Un = n and let Vn = f (Un) with n an integer and f a map.

The sequence U0, U1, U2, ..., Un contains p prime numbers.

The sequence V0, V1, V2, ..., Vn contains k prime numbers.

I found an example of increasing Vn which gives k ~ 1.5 * p in Excel.

And instead of looking for a logic of prime numbers in the list U0, U1, U2, ..., Un, I will rather look for a logic between prime numbers in the list V0, V1, V2, ..., Vn where there are more prime numbers in this list.

If I find this logic, I can write k as a function of n, then p as a function of n, to find a logic of the distribution of prime numbers in the set of integers.

Cordially.

Here I can formulate a conjecture on prime numbers:

Let Un and Vn be two increasing sequences of integers and Vn> Un which are defined on the pdf sent.

and up and vp the sum of quantity of prime numbers up to n,

For example there are 2 3 5 which are prime in Un so u5 = 1 + 1 + 1 = 3 and v5 = 4 because there are 4 prime numbers up to 5 in Vn.

The conjecture says if vn is unique (repeats only once) in the list of prime sums of Un (u0, u1, u2..un) and Un + Vn (u0 + u0, u1 + u1, u2 + u2..un + vn) then Vn is prime.

Can we prove or refute this conjecture?

PDF:

thematiques.net :: Shtam

With this conjecture I can even estimate where there is a large prime number, because we know the distribution of prime numbers up to n and therefore we can evaluate the sum of primes of Un and that of Vn ~ 1.5 of One.

We check that vn-1, vn, vn + 1 are different to find a prime Vn.