Definition: In the gap between any two consecutive odd primes we have one or more composite numbers. We define the largest of among all the prime factor of these composite as the maximal prime factor of the gap.
Claim: Every prime is a maximal prime factor for some prime gap.
Experimental data for $p \le 10^5$ supports this claim. I am looking for a proof or disproof.
from Hot Weekly Questions - Mathematics Stack Exchange
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