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2021-11-23: 3299 spiral and fibonacci primes

The spiral

On page 15 (starting with unsolved pages) the following matrix can be seen:

3258 3222 3152 3038
3278 3299 3298 2838
3288 3294 3296 2472
4516 1206 708 1820

I found this Google Doc to be the best explanation of this spiral so far:

[HTTP] Google Document

In short, the starting point is 3299 (row 2, col 2).

Then the spiral goes down all the way to 708, from where the numbers start to increase.

The general rule of this spiral is:

N(n) = Prime(Fib(n))

if N(n)<=3301: N(n) = 3301-N(n)
else: N(n) = N(n)-3301

One caveat: actual Fibonacci sequence uses two 1's.

Here, one of the 1's is skipped.

Definitions

For lack of better terms, I will use these:

FIBPRIMES is a sequence of FP(n) = Prime(Fib(n)), where Fib(n) starting with Fib(0) = 0, Fib(1) = 1, Fib(2) = 2, after which normal Fibonacci rules apply. Also, Prime(0) = 2; that is 1 is not a prime.

"AFFECTION" BY 3301: I use this term to refer to the operation where number is subtracted from 3301 if it's less than 3301, and otherwise 3301 is subtracted from that number.

Extending the spiral

My idea was to extend this spiral as far out as I could. That's not easy because Fibonacci numbers rise pretty fast, and even for the 30'th member of the resulting sequence you will need to find 1346269th prime number.

I procrued a total of 36 members of the sequence. They can be found in the following CSV file:

fibprime_sequence.csv

Of these number, I believe the following sequence to be of most importance:

22;21;19;17;11;1;10;3;20;22;25;7;22;12;17;21;26;1;8;20;16;26;19;12;28;1;22;3;11;25;6;4;26;3;0;10

This is a sequence of fibprimes, "affected" by 3301 and taken modulo 29.

What now

I don't know what now. I'm pretty sure this sequence will somehow be needed at some point, becuase why else would the original spiral be there?

Maybe it would be needed to further extend this sequence, but that probably will need a lot more resource than I have.