If we can probe that there is a set that always will be denser than

6ab+-a+-b then twin primes will be infinite. I asked myself if it is

possible to get a candidate. The first option was the 3ab+-a+-b set. In

fact, all odds numbers are of this form and only very few even numbers are

of the form. I divided some 6ab+-a+-b integers by the corresponding

3ab+-a+-b and 6ab+-a+-b are in average two times larger. It was obvious for

me that one set is denser than de other, but how. Checking up to one hundred

I realized that the integers that not were equal to 3ab+-a+-b correspond

exactly twice non 6ab+-a+-b. I donĀ“t kow if someone has information about

this approach.

Then if g is not equal to

6ab+-a+-b, 2g wont be equal to 3ab+-a+-b. It apalled me because it

reflects the two times larger correspondence in a very weird way. The

6ab+-a+-b

problem seems to exeed the twin primes distribution.

Kind regards,

Alberto Zelaya

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