Schinzel-Sierpinski conjecture

Statement

The name Schinzel-Sierpinski conjecture is used for two related conjectures:

• For any positive rational number $r$, there exist prime numbers $p,q$ such that $r={\frac {p+1}{q+1}}$ (in fact, we would expect there to be infinitely many such prime pairs).
• For any positive rational number $r$, there exist prime numbers $p,q$ such that $r={\frac {p-1}{q-1}}$ (in fact, we would expect there to be infinitely many such prime pairs).

References

• Computations related to the conjecture