S17. 5 prime-related { Discrete Series }

An Approach to Prime Numbers , the L.C.M. , and the Zeta Functions

Section XVII - Summarizing the 5 prime-related { Discrete Series }

Let us now list the 5 prime-related series } we have used in this paper :
- Series #1 --- The { Prime Number Series } :
  - { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , .......... }
- Series #2 --- The { Prime Product Series } :
  - { 2 , 6 , 30 , 210 , 2310 , 30030 , 510510 , 9699690 , 223092870 , 6469693230 , ........ }
- Series #3 --- The { Prime and Power-of-Primes Series } :
  - { 2 , 3 , 4 , 5 , 7 , 8 , 9 , 11 , 13 , 16 , 17 , 19 , 23 , 25 , 27 , 31 , ........ }
- Series #4 --- The { L.C.M. Series } :
  - { 2 , 6 , 12 , 60 , 420 , 840 , 2520 , 27720 , 360360 ,720720 , 12252240 , ........ }
- Series #5 --- The { L.C.M.-based Differential-Factor Series }
  - { 2 , 3 , 2 , 5 , 7 , 2 , 3 , 11 , 13 , 2 , 17 , 19 , 23 , 5 , 3 , 31 , ........ }
And on the usage of the Series :
- { Prime Counting } is traditionally based on { Series #1 } .
- Riemann's [ f(x) function ] is based and rooted in { Series #3 } .
- The Author used { Series #4 } and { Series #2 } in this equation :
  - in Section V .
- In the Fast-Track procedure to identify { prime numbers } in Section VII , we used { Series #2 } .
But { Series #5 } is interesting because it also contains information { multiplex relative-logariths } , such as :
- [ 2^16 ] < [ 17^2 ] < [ 2^17 ] ;
- [ 3^5 ] < 2^16 ] < [ 3^6 ] ;
  
  etc. .

Let us not forget Chebyshev , and bring-in the 6th Series :
- the [ Factorial Series ] .