Subject: prime difference function,list length of prime differnce function, and sets of twin primes,cousin primes,sexy primes, dixie primes
The prime difference function and sets of twin primes might be useful.I see that Wolfram and Wikipedia uses the common  slang names. Thank you.  
1. prime gap function from 0 to N ,  PrimeDifferenceFunction,gaps between prime numbers, set of prime gaps,  primes_gaps_LowerThan
2. prime gap function,  PrimeDifferenceFunction,set of prime gaps from some lower limit to some upper limit
3. prime gap function, PrimeDifferenceFunction, number or list set size<list llength?> of prime gaps from some lower limit to some upper limit
4. prime twin function from 0 to N, primes separated by 2 ,set of prime twins,  primes_twins_LowerThan
5. prime twin function, primes separated by 2 ,set of prime twins from some lower limit to some upper limit
6. prime twin function, primes separated by 2 ,number or list set size of
  prime twins <list llength?> from some lower limit to some upper limit
 8. prime cousin primes function from 0 to N, primes separated by 4 ,set of prime twins,  primes_twins_LowerThan
 9. prime cousin primes function, primes separated by 4 ,set of prime twins from some lower limit to some upper limit
 10. prime cousin primes function, primes separated by 4 ,number or list set size of prime twins <list llength?> from some lower limit to some upper limit
OEIS  reports or uses prime quadro function as primes separated by 4 , omitting primes separated by 2
11. prime sexy function from 0 to N, primes separated by 6 ,set of sextos  ,  primes_sexy_twins_LowerThan
12. prime sexy function, primes separated by 6 ,set of prime sextos from some lower limit to some upper limit
13. prime sexy function, primes separated by 6 ,number or list set size of sextos   <list llength?> from some lower limit to some upper limit
OEIS  reports or uses a prime sexy function as primes separated by 6 , omitting primes separated by 2 and 4
14, prime deca function from 0 to N, primes separated by 10 ,set of dixie  ,  primes_dixie_LowerThan
15. prime deca function, primes separated by 10,set of prime dixie from some lower limit to some upper limit
16. prime deca function, primes separated by 10 ,number or list set size of sextos   <list llength?> from some lower limit to some upper limit
OEIS  reports or uses a prime dixie function as primes separated by 10 , omitting primes separated by 2, 4,6
17. References.
Latin is years behind me, best check with OEIS website for their current nomenclature, which can change rapidly. I see that Wolfram and Wikipedia uses the common  slang names.
https://en.wikipedia.org/wiki/On-Line_Encyclopedia_of_Integer_Sequences
https://en.wikipedia.org/wiki/Twin_prime
https://en.wikipedia.org/wiki/Cousin_prime
https://en.wikipedia.org/wiki/Sexy_prime
https://mathworld.wolfram.com/PrimeGaps.html
https://mathworld.wolfram.com/PrimeDifferenceFunction.html
https://oeis.org/
https://oeis.org/A077800, twin primes
https://oeis.org/A031924
https://oeis.org/A007693
https://oeis.org/A023201, sexy primes
https://mathworld.wolfram.com/SexyPrimes.html
https://mathworld.wolfram.com/CousinPrimes.html
https://mathworld.wolfram.com/TwinPrimesConstant.html
https://mathworld.wolfram.com/BrunsConstant.html
https://mathworld.wolfram.com/TwinPrimes.html
https://mathworld.wolfram.com/TwinPrimeConjecture.html
Cousin prime
Prime gap
Prime k-tuple
Prime quadruplet
Prime triplet
Sexy prime
https://www.sciencedirect.com/science/article/pii/0022314X87900527?via%3Dihub
https://wiki.tcl-lang.org/page/Gauss+Approximate+Number+of+Primes+and+eTCL+demo+example+calculator?V=183
            # reference On-Line Encyclopedia of Integer Sequences website
            # OEIS A077800 discussed that the twin prime sets <p,p+2> are
            # (3, 5), (5, 7), (11, 13), (17, 19), 
            # (29, 31), (41, 43), (59, 61), (71, 73),
            # (101, 103), (107, 109), (137, 139)...
            # OEIS A275021 has  samples of <p,p+4> and omits pairs of <p,p+2>
            # 79, 83, 127, 131, 163, 167, 379, 383, 397, 401, 439, 443,...
            # list_twin_primes 75 135 4 returns 79 83 103 107 127 131
            # OEIS A023201 has some samples of <p,p+6> 
            # 5, 7, 11, 13, 17, 23, 31, 37, 
            # 41, 47, 53, 61, 67, 73, 83, 97, 101
