This chalkboard should have been an appendix to Chalkboard #3 on Classification of Prime Numbers. I previously defined three types of primes which were used to classify the period length of the Perrin sequence modulo (p).
If we start to look for rational solutions mod (p) to the elliptic curve defining the Perrin sequence the reason for this classification becomes apparent.
The ideas for this chalkboard came after reading “Fearless Symmetry” by Avner Ash and Robert Gross (Princeton University Press) 2006.
Board12_Elliptic Curves Over the Rational Number Field
Perrin Sequences My Chalkboard 