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Jul
31
comment Is there a theorem or conjecture that specifies a balanced prime must be multiple of 3# distance from neighboring primes?
Thanks, @Gerry Myerson! I don't have reputation to upvote these answers, but thank you everyone for the links and help.
Jul
31
comment Is there a theorem or conjecture that specifies a balanced prime must be multiple of 3# distance from neighboring primes?
Thank you, that's the right picture!
Jul
31
awarded  Scholar
Jul
31
accepted Is there a theorem or conjecture that specifies a balanced prime must be multiple of 3# distance from neighboring primes?
May
19
revised Is there a theorem or conjecture that specifies a balanced prime must be multiple of 3# distance from neighboring primes?
added 35 characters in body
May
19
awarded  Editor
May
19
revised Is there a theorem or conjecture that specifies a balanced prime must be multiple of 3# distance from neighboring primes?
Editing question to provide answer provided by the commenters
May
19
comment Is there a theorem or conjecture that specifies a balanced prime must be multiple of 3# distance from neighboring primes?
@AndréNicolas Thank you! I had read that, but didn't properly realize that CPAP-3 is a special case of AP-3. And apparently the Green-Tao theorem says: "If an AP-k does not begin with the prime k, then the common difference is a multiple of the primorial k# = 2·3·5·...·j, where j is the largest prime ≤ k."
May
19
comment Is there a theorem or conjecture that specifies a balanced prime must be multiple of 3# distance from neighboring primes?
@MarkBennet yes, 3,5,7 is an exception, but I think that would be covered in the theorem for minimum separation of a balanced prime (besides 5, all others have a minimum separation of 3#)
May
19
asked Is there a theorem or conjecture that specifies a balanced prime must be multiple of 3# distance from neighboring primes?
May
19
awarded  Autobiographer