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I was trying to get an overview of the status and activity for Proth prime search with small k values.
I find the small k most interesting because (1) they are more "beautiful" because they are {a more round number} plus one, and (2) they are more often divisors of Fermat numbers of (extended) generalized Fermat numbers.
k=3:
This seems to be well handled by 321 search (the plus half of it). See /stats_321_llr.php
k in { 5, 7, 9 }:
There is no "521 search" (although 521 is a nice name). Who votes for one?
These multipliers are not in the MEGA stats page /stats_mega_llr.php, but it appears the "ordinary" PPS project goes beyond the megaprime level for these k, see /stats_pps_llr.php. They stand at 6M, 6M, and 4M for the k values for resp. 5, 7, and 9.
Is it true that these will be handled by PPS (not MEGA)? When will these small k be prioritized again?
k in { 11, 13 }:
On the ordinary PPS stats page, these stop at the megaprime level, but 11 and 13 are included in the MEGA stats page, /stats_mega_llr.php. They stand at k equal to 3.6M there.
However, on http://www.prothsearch.com/riesel1.html, under 11 and 13, we see 5.5M and 5M, respectively, in the square brackets. Is someone outside PrimeGrid taking the lead here? That would be a shame.
Will k=11 and k=13 be run under MEGA in the future? When will they become active again (is there a plan)?
k in { 15, ..., 99 }:
On PPS, these currently stand at the megaprime threshold. On the MEGA stats page, these k values are absent? A few k limit values on prothsearch.com are higher than the megaprime limit (which is about k=3.32M).
For some of these k values, on Caldwell's Top 5000, the record for that k is discovered by Serge Batalov outside PrimeGrid.
Will k between 15 and 99 be run on the MEGA project in the future?
k in { 101, ... }:
Here we have a gap between PPS (which is still below the megaprime level) and MEGA. It looks like both projects cover these exponents (up to 1200, and from there covered by PPSE).
When k>100, the primes are less spectacular (my opinion), and less like to divide Fermat numbers (unsurprising empirical fact).
/JeppeSN | 
