My Prime Numbers Axiom

My Prime Numbers Interval Axiom

There is maximally 17 prime numbers in each interval of the form:

interv(i) := [100*(i-1)+1, 100*i], i ∈ Ν\{1,2}

for i ∈ {1,2}, we have:

• interv(1) := 25, and

• interv(2) := 21.

Thus,

∀i ∈ Ν\{1,2} ⇒ #Primes in interv(i) ≤ 17

I challenge you to prove the contrary!

Here is a start example for you:

30000 investigated intervals sorted here with the frequency of primes

Standard graphic that investigate the number of primes for the first 30000 intervals of the form [100(i-1)+1, 100i]

List of the number of primes for the first 32 intervals

Here is the list of the prime numbers for the first 6 intervals:

Denote here, that I used a special technique to find them. This, will be explained in a future post.

 

* Some mistakes concerning the graphics, prime list and some incorrect statement have been corrected!