# Recycling (spin 9)

This section is referring to *wiki page-27* of *main section-5* that is *inherited * from *the spin section-main* by *prime spin-80* and *span-31* with *the partitions* as below.

- Feeding (spin 3)
- Entrypoint (spin 4)
- Mapping (spin 5)
- Keyring (spin 6)
- Enneagram (spin 7)
- Twisting (spin 8)
- Recycling (spin 9)
- Exchange (spin 10)
- Dimensions

This progression 41,43,47,53,61,71,83,97,113,131 whose general term is

, is as much remarkable since the41+x+xxare all prime numbers40 first terms(Euler's letter to Bernoulli).

```
1st layer:
It has a total of 1000 numbers
Total primes = π(1000) = 168 primes
2nd layer:
It will start by π(168)+1 as the 40th prime
It has 100x100 numbers or π(π(10000)) = 201 primes
Total cum primes = 168 + (201-40) = 168+161 = 329 primes
3rd layer:
Behave the same as 2nd layer which has a total of 329 primes
The primes will start by π(π(π(1000th prime)))+1 as the 40th prime
This 1000 primes will become 1000 numbers by 1st layer of the next level
Total of all primes = 329 + (329-40) = 329+289 = 618 = 619-1 = 619 primes - Δ1
```

Plottng ** 40th prime scheme** of the three (3) layers with all the features of 3rd prime identity as explained above then they would form their recycing through the three (3) times bilateral 9 sums as shown below.

*89^2 - 1 = 7920 = 22 x 360 = 66 x 120 = (168 - 102) x 120*

I wondered if that property might hold for the incremental powers of phi as well. For this reason I chose to see numbers in the hexagon as quantum, and truncate off the decimal values to determine which integer cell they land in.

That is what I found. Phi and its members have a pisano period if the resulting fractional numbers are truncated.

*FeynCalc* is a Mathematica package for symbolic evaluation of Feynman diagrams and algebraic calculations in quantum field theory and elementary particle physics.