Okay, these have been eliminated by the work of 17-or-bust:

k = 9694 (4847)
k = 19388 (4847)
k = 38776 (4847)
k = 77552 (4847)
k = 10718 (5359)
k = 21436 (5359)
k = 42872 (5359)
k = 38498 (19249)
k = 76996 (19249)
k = 55306 (27653)
k = 38498 (19249)
k = 56866 (28433)

Similarly, we know there is no prime known for the following because 17-or-bust (and others) have failed to find a prime for the corresponding odd k:

k = 20446 (10223)
k = 40892 (10223)
k = 42362 (21181)
k = 45398 (22699)
k = 49474 (24737)
k = 67322 (33551)

6128 is the continuation of 766, 1532, 3064 rather than 6122, so this eliminates 12256, 24512, and 49024 as well. I'll bet we can eliminate most of the rest of these with the list of primes at:
[url]http://www.prothsearch.net/sierp.html[/url]
as there are a number of primes there with n values > 50,000.