[seqfan] unique primes: should A040017 and A051627 be truncated?

[Max Alekseyev]

SeqFans,

We have well-defined sequences A007498 and A007615 that list smallest known
periods and the corresponding unique primes, respectively. These sequences
are in order (unless there was a computational error).

The related sequence A040017 makes an attempt to sort the terms of A007615,
however as soon as the terms become big we lose guarantee that there are no
unknown primes appearing in between of the known ones.
That is, the currently listed terms of A040017 and its counterpart A051627
become conjectural at best.

Using the largest known term of A007498, which is 198552, we have a
guarantee that all unique primes below it are known. Perhaps, we can push
this bound a bit further, but I highly doubt we can compute all unique
primes below, say, (10^19-1)/9 currently listed as A040017(13).

Do I miss something?
If not, both A040017 and A051627 should be truncated to guaranteedly known
initial terms.

Regards,
Max