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Old 2021-07-20, 10:40   #1
robert44444uk
 
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Jun 2003
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Default 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
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Old 2021-07-22, 13:26   #2
Bobby Jacobs
 
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Quote:
Originally Posted by robert44444uk View Post
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.
There is also the repeating gap of 2 between the primes 3, 5, 7.
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Old 2021-07-24, 07:45   #3
Raydex
 
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Quote:
Originally Posted by robert44444uk View Post
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

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
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Old 2021-07-26, 09:37   #4
robert44444uk
 
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Quote:
Originally Posted by Raydex View Post
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
Ah!! Of course! I forgot the law of small integers.

It is also a CPAP-3.
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Old 2021-07-27, 14:23   #5
robert44444uk
 
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I've completed 5e13 to 6e13, with no double gap >312.

I'm now taking 6e13 to 3e14.
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