# Thread: a new prime number conjecture

1. Good morning all,

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

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.  2.

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