Yes, I did see your posts #364 and #371 and I'll look into it.

But it's going to take me a few days to run the data analysis programs.

The execution times are very long and I don't understand why.

I'll try to shorten these execution times.

I also think that to better notice things, I'll have to modify the program that gives the output :

Code:

base 2 prime 197748738449921 exponent 265
base 2 prime 197748738449921 exponent 530
base 2 prime 242099935645987 exponent 198
base 2 prime 242099935645987 exponent 396
base 2 prime 332584516519201 exponent 19
base 2 prime 332584516519201 exponent 382

In order for the output to become something like this :

Code:

base 2 prime 197748738449921 exponent 265 at index 1
base 2 prime 197748738449921 exponent 530 at index 1
base 2 prime 242099935645987 exponent 198 at index 1
base 2 prime 242099935645987 exponent 396 at index 1
base 2 prime 332584516519201 exponent 19 at index 1
base 2 prime 332584516519201 exponent 382 at index 1

Or something more like your idea that you present in post #371, like this :

Code:

prime 197748738449921 shows up 2 times (265:i1, 530:i1).
prime 242099935645987 shows up 2 times (198:i1, 396:i1).
prime 332584516519201 shows up 2 times (191:i1, 382:i1).

Indeed, for the other bases, one does not always find the repetitions of prime numbers at index 1, and besides, it is generally not at index 1 anymore.

More curious : by manually and laboriously examining (hence the need to automatically examine) the data in your file attached to post #374, it even happens that a large prime number repeats itself twice in two terms at two indexes of the same sequence.

And this may be a coincidence, but I prefer to be sure !

Then I also want to know if large prime numbers repeat more than twice in a single sequence and if so, at which indexes.