New project : Define $$f(n):=\prod_{j=1}^n F_j$$ where $F_j$ denotes the $j$-th Fibonacci-number. $f(n)-1$ is prime for $n=4,5,6,7,8,14,15$ and $f(n)+1$ is prime for $n=1,2,3,4,5,6,7,8,22,28$. Are there more primes of the form $f(n)\pm1$ ?
Ok, $n=360$ is very large, we should check if there's like a list of primes common among a certain bunch of multiples . For example , is there a predictable sequence of $n$ for which $f(n)+1$ or $f(n)-1$ is a multiple of $3/5/7$ etc.
We can then start ruling out all such $n$. Hopefully there will be some modulo pattern to help us.
Rather the opposite holds. Every prime factor of a fibonacci-number upto $F_n$ CANNOT be a prime factor of either $f(n)-1$ or $f(n)+1$. So, we have many candidates.
But the sequence $f(n)$ grows of course very quickly. Hence it can take a while to get the next PRP.
To be more precise : Presieving will not remove many candidates, but some gain of speed might be possible. Maybe , PFGW allows to eveluate products , factordb seems not to support it.
Maybe, someone in the mersenne forum knows a syntax for PFGW.
I do not think that there is a closed form expression readable by factordb or PFGW, right ?
Sure, why not? Let me know what exactly to print out, I can get it done and let you know how it's done.
I mean to say : I'll create the program and find you an online IDE where you can run it get the output and put it into factordb. Python will do the string-generation very easily.
By the way, I need to leave, so you can leave the results here and I will definitely take a look at them tomorrow. Meanwhile, my thread will be free tomorrow so I'll be able to work with yafu and LLR if required. Thanks.