20210720, 10:40  #1 
Jun 2003
Oxford, UK
11110011001_{2} Posts 
Repeating gaps
With the group's current computing resources it should be possible to take the following sequence and extend it
https://oeis.org/A052187 So 47,53,59 is the first sequence of primes with a repeated gap of 6. Repeated gaps are all 0mod6. This is easy to prove. The highest known members of the sequence are 46186474937633 46186474937957 46186474938281, differing by 324. However no repeating gap of 318 is know below 5e13 according to Johnson and Resta. I might have a look at 5e13 to 6e13 
20210722, 13:26  #2 
May 2018
11100000_{2} Posts 

20210724, 07:45  #3  
Nov 2020
Massachusetts, USA
2·11 Posts 
Quote:
A minor correction to your original comment: Repeated gaps are all 0mod6 except for the triplet 3, 5, 7. Also, I believe the name for this is "balanced primes." You can read more about that here. https://en.wikipedia.org/wiki/Balanced_prime 

20210726, 09:37  #4  
Jun 2003
Oxford, UK
5×389 Posts 
Quote:
It is also a CPAP3. 

20210727, 14:23  #5 
Jun 2003
Oxford, UK
5·389 Posts 
I've completed 5e13 to 6e13, with no double gap >312.
I'm now taking 6e13 to 3e14. 
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