Problems & Puzzles: Conjectures

Conjecture 86.  The Majid's Conjecture

Majid Azimi wrote on October 3, 2020:

Recently I came up with the following conjecture, not studied previously, as far as I know:

Conjecture:

"There is at least one couple of twin primes between the square of consecutive odd number, (2n-1)^2 and (2n+1)^2, for n=>1"

I have tested for n<=10^9 and the conjecture holds. See here all the data I have computed, shown by ranges up to n<=10^6.

Two examples:

n 2n-1 2n+1 (2n-1)^2 (2n+1)^2 Quantity of couples
 of twin primes
1 1 3 1 9 2; (3,5), (5,7)
2 3 5 9 25 2; (11,13), (17,19)

Not a proof of my conjecture, but just a graphical description of the behavior of the Count of couples of twin primes (Q) between (2n-1)^2 and (2n+1)^2, I offer you the following graph of data:

Fig A: Count of couples of twin primes between the square of consecutive odd integers
(
Vertical line is count of couple twins between (2n-1)^2 and (2n+1)^2 and horizontal line is n, for n=>1)

 

Q1. Can you tell if this Conjecture has been proposed and/or studied before by others?

Q2. Can you find a counterexample, or prove this conjecture.


 

Records   |  Conjectures  |  Problems  |  Puzzles