I am new here and have probably missed some history, but why do we have ports for GFN32768, GFN65536 (n=15,16) and for GFN262144, GFN524288 (n=18,19) while we have no testing of GFN131072 (n=17)?

Is testing of GFN131072, that is b^(2^17) + 1, being done elsewhere?

/JeppeSN

Not to take this as 100% authoritative answer (my memory if not of most reliable) but to get idea since I was involved in early stages of GFN sieving and prime search.

As far as I can remember, David Underbakke has n=17 reserved and is doing search in this range for couple of years. So yes, it is being done elsewhere and PrimeGrid is doing other ranges.
David found first prime for n=17 back in 2009: 386892^131072+1.

David's AthGfn64 was used for sieving and was enhanced, adjusted (PrimeGrid factoring file requirements) and optimized when used in PG's sieving. Looking into my old e-mails, that was in 2009 as well (before n=17 prime). I've done most of the initial sieving on CPUs and low n, high b (up to b<100M) primality tests using CPUs as well (in pre-GPU era).
Later, sieving was ported to CUDA GPU and GFNSvCUDA was introduced. You can imagine it was a game changer.
And later on, GeneferCUDA for PRPNet and BOINC was introduced, a major game changer.
____________
My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186

Not to take this as 100% authoritative answer (my memory if not of most reliable) but to get idea since I was involved in early stages of GFN sieving and prime search.

As far as I can remember, David Underbakke has n=17 reserved and is doing search in this range for couple of years. So yes, it is being done elsewhere and PrimeGrid is doing other ranges.
David found first prime for n=17 back in 2009: 386892^131072+1.

David's AthGfn64 was used for sieving and was enhanced, adjusted (PrimeGrid factoring file requirements) and optimized when used in PG's sieving. Looking into my old e-mails, that was in 2009 as well (before n=17 prime). I've done most of the initial sieving on CPUs and low n, high b (up to b<100M) primality tests using CPUs as well (in pre-GPU era).
Later, sieving was ported to CUDA GPU and GFNSvCUDA was introduced. You can imagine it was a game changer.
And later on, GeneferCUDA for PRPNet and BOINC was introduced, a major game changer.

GeneferCUDA came before GFNSvCUDA.

Reservations for GFN ranges until May 2004 appear to have been organised by Yves:
http://yves.gallot.pagesperso-orange.fr/primes/status.html

Anyone know where more recent reservations are listed for N=17 and N=21?

On February 2013 Underbakke found 689186^131072+1
http://primes.utm.edu/primes/page.php?id=111122
Guess he hasn't been idle.