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Q: Largest integer interval such that for all primes $p \in I$, we have that $p = 2 \pmod q$ for some $q \in Q$ a fixed finite set of primes?

MathCrackExchangeGiven a finite set of prime numbers $Q = \{ q_1, \dots, q_n\}$. What is the maximum size of any integer interval $I$ of consecutive integers such that for all $p \in I \cap \Bbb{P}$, $p =2 \pmod {q_i}$ for some $q_i \in Q$? This relates to the twin prime conjecture obviously.

 
7 hours later…
07:13
@KReiser same author, similarly topic: math.stackexchange.com/q/4753172/42969
 
5 hours later…
12:28
@KReiser undelete-voted !
 
1 hour later…
13:38
please close/delete - the answerer admits it is opinion-based , but nevertheless answered it !
14:52
two reopen-votes:( - we need downvotes and anyway more helpers. By the way : Is the strike still on ?
 
1 hour later…
17:39
Duplicate (which is also a very basic question) with an accepted answer.
 
3 hours later…
20:38
A case of a no-effort question where solutions seem to abound: math.stackexchange.com/q/4753526/29335. Close maybe?
 
2 hours later…

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