If you hold non-mainstream mathematical views and want to ask questions about them, what you should do is be extremely clear and specific about what you're asking.
Many mathematicians have had very negative experiences engaging with people that have unusual mathematical views and defend them by:
- relying on intuitive notions rather than rigorous definitions.
- describing procedures too vague to tell what exactly they do and therefore impossible to find a specific flaw in without asking many clarifying questions.
- moving the goalposts when a contradiction is found.
So we've learned to react poorly to signs that a question might start going in these directions.
You've actually done reasonably well in avoiding these pitfalls: your question asks when a well-specified algorithm will always produce certain specific input. (I think you'd have done better by being more specific about the pattern you see: that for all sufficiently large $n$, the $2^{\text{nd}}$ element of the $n^{\text{th}}$ row is equal to the $1^{\text{st}}$ element of the $(n+2)^{\text{th}}$ row. But that's a minor quibble.) As a result, you've gotten a net positive response in votes, and answers that address your question.
I suspect that downvotes and criticism are due to your notion of "random" sequences, which is not nearly as well-specified. For example, the set $L$ actually described by the first paragraph is merely the set of eventually-periodic sequences, which definitely does not include the sequence of all primes. A computer with a finite amount of memory will not be able to generate the sequence of prime numbers, since eventually it will have too little memory to hold the $n^{\text{th}}$ prime number, much less test it for primality. Your conclusion also seems much stronger than warranted, which is a bit of a warning sign.