Cousin primes cannot be of this form.

[Davide Rotondo]

Hello all SeqFan members. To obtain the various k suitable for first cousins, I started from Balestrieri's consideration for twin primes. However, these are the forms:
k1 = 12*x*y - 2*x - 2*y + 1
k2 = 12*x*y + 2*x + 2*y + 1
k3 = 12*x*y + 2*x - 2*y - 1
k4 = 12*x*y - 2*x + 2*y - 1
The odd values ​​of the complement sequence k1 U k2 U k3 U k4, multiplied by 3, are the average of two first cousins.

What do you think? Can I propose this to the encyclopedia?

Davide

[Davide Rotondo]

Dear, is this equal to prove that exist infinite cousin primes?

Davide

[M F Hasler]

On Thu, Jun 18, 2026 at 4:13 AM Davide Rotondo <david...@gmail.com> wrote:

Dear, is this equal to prove that exist infinite cousin primes?

No,

a) No prime is infinite. You mean "infinitely many".

b) You didn't prove there are infinitely many.

You are just stating that the average of cousin primes are those m=3(2k+1)

for which m-2 and m+2 isn't the product of two odd integers

(which is equivalent to say that they are prime).

-M.