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 $r={\frac {p+1}{q+1}}$. A stronger version of the conjecture asserts that there are infinitely many such pairs of prime numbers.
• For any positive rational number $r$, there exist prime numbers $p,q$ such that $r={\frac {p-1}{q-1}}$. A stronger version of the conjecture asserts that there are infinitely many such pairs of prime numbers.

References

• Computations related to the conjecture