The Symmetric Prime Tuples (SPT) project is an continue of the T. Brada Experimental Grid project
https://boinc.tbrada.eu/
The results of this project are available in the "Prime Tuple Database"
https://boinc.tbrada.eu/spt/explore.php

The main definitions on the topic of the project can be found on the page "Problem 62. Symmetric k-tuples of consecutive primes"
http://www.primepuzzles.net/problems/prob_062.htm

Basic definitions

Definition 1
A prime k-tuple is a finite collection of values (p + a1, p + a2, p + a3, …, p + ak),
where p, p + a1, p + a2, p + a3, …, p + ak are prime numbers, (a1, a2, a3, …, ak) are pattern. Typically the first value in the pattern is 0 and the rest are distinct positive even numbers. [1]
We consider the k-tuple, where p + a1, p + a2, p + a3, ..., p + ak are consecutive primes.
Definition 2
k-tuple (p + a1, p + a2, p + a3, ..., p + a [k / 2], p + a [k / 2+1], ..., p + a [k-2], p + a [k-1], p + ak) for k even, is called symmetric, if the following condition is satisfied:
a1 + ak = a2 + a[k-1] = a3 + a[k-2] = … = a[k/2] + a[k/2+1]
Example
symmetric 8-tuple
(17 + 0, 17 + 2, 17 + 6, 17 + 12, 17 + 14, 17 + 20, 17 + 24, 17 + 26)
Shortened we write this:
17: 0, 2, 6, 12, 14, 20, 24, 26
Definition 3
k-tuple (p + a1, p + a2, p + a3, ..., p + a [(k-1) / 2], p + a [(k-1) / 2 + 1], p + a [(k-1) / 2 + 2], ..., p + a [k-2], p + a [k-1], p + ak) for k odd called symmetric, if the following condition is satisfied:
a1 + ak = a2 + a[k-1] = a3 +a [k-2] =…= a[(k-1)/2] + a[(k-1)/2+2] = 2 a[(k-1)/2+1]
Example
symmetric 5-tuple
18713: 0, 6, 18, 30, 36
(See in [2])
Definition 4
The diameter d of k-tuple is the difference of its largest and smallest elements. [1]
Example
8-tuple
17: 0, 2, 6, 12, 14, 20, 24, 26
It has a diameter d = 26.

https://www.primepuzzles.net/problems/prob_062.htm

See topic
https://boinc.progger.info/odlk/forum_thread.php?id=259#12666

Also
https://boinc.progger.info/odlk/forum_thread.php?id=291
https://boinc.progger.info/odlk/forum_thread.php?id=226#8447