Russian amateur mathematician Viktor Voevodov put forward a conjecture generalizing the conjecture about twin primes. He suggested (in a slightly different formulation) that for any finite increasing sequence of primes, there are infinitely many sequences of primes with the same distances between neighboring primes as the original one (it is supposed that the number of primes < first prime).
The conjecture about twin primes is obtained as a special case, if we proceed, for example, from the sequence 3,5.
Perhaps this kind of hypothesis has already been expressed by someone earlier. What is known about it?