Quote:
Originally Posted by kar_bon
Previous is a double post from your own thread!

Yes, I want to let more people know this conjecture, as Riemann hypothesis and abc conjecture and Schinzel's hypothesis H
This conjecture would imply all
Sierpinski conjectures and
Riesel conjectures in CRUS to every base b>=2, also the dual Sierpinski conjecture (whether 78557 is the smallest odd number k such that 2^n+k is composite for all n>=1) and the dual Riesel conjecture (whether 509203 is the smallest odd number k such that 2^nk is composite for all n>=1), and also imply there are infinitely many such primes:
* Mersenne primes
* Fermat primes
* Generalized repunit primes (b^n1)/(b1) to every base b>=2 not of the form m^r with r>1
* Generalized negarepunit primes (b^n+1)/(b+1) to every base b>=2 not of the form m^r with odd r>1 and not of the form 4*m^4 with integer m
* Generalized Fermat primes b^(2^n)+1 to every even base b>=2 not of the form m^r with odd r>1
* Generalized half Fermat primes (b^(2^n)+1)/2 to every odd base b>=2 not of the form m^r with odd r>1
* Williams primes of the 1st kind (b1)*b^n1 to every base b>=2
* Williams primes of the 2nd kind (b1)*b^n+1 to every base b>=2 (not always true if b1 is of the form m^r with odd r>1 or of the form 4*m^4 with integer m)
* Williams primes of the 3rd kind (b+1)*b^n1 to every base b>=2