-> Sequences.lisp aims to eventually solve Goldbachs Conjecture by proving that Goldbachs comet occurs in a sequence or algorithm that can be computed. If something can be computed with a algorithm, it's a proof. Just by looking at the picture below, it's quite clear that there is a pattern/sequence and that Goldbachs Conjecture is not just a conjecture. Since there is an infinate number of primes you cannot test every prime in existance.
Goldbach's comet also shows an obvious pattern that looks like the upper right side of a hyperbola. This means that the sums of primes can be predicted! It would also give a valid reason of why the greek mathematicians were so obsessed with hyperbolas and primes.
Solving this problem is still a work in progress, I have not even completed a single book on lisp yet. But I am working on this when I get bored of the book. To see my progress through the book please see https://github.com/beans816/learning-lisp
Thank you :) !
Common Lisp predicate of a prime number using the ancient algorithm of the Sieve of Eratosthenes. If you cannot define a prime through a sequence, you define a prime number by the number of its prime factors.
-> Primes don't occur in a sequence that I know of. They are found using Eratosthenes algorithm since this works perfectly every time and uses logic.
In the file 'PrimesofCyrene.lisp' you will see these functions:
(primep n)
(Sieve-of-Eratosthenes list)
Think of the functions quite literally as a Sieve and then you will understand how to find prime numbers! Or think of it like gold panning.
I need to fully understand sequences to continue understanding goldbachs conjecture. So I am making a library of functions that return the sequence rule when given a list of numbers. When I figure it out in it completed-ness maybe I can just try it on prime numbers and see if there is a sequence.