The number of candidates for n < 1,000,000 seems so small for p < 21e12. I sieved k=1281979 up to p = 312e12 and was left with nearly 15,000 candidates for n < 1,000,000.
And as rogue said, definitely use sr1sieve. It is by far the fastest for this type of search. For the Proth test, do you use LLR2? It has Gerbicz error correction which is very useful when working alone (i.e. no double checking).
And best of luck to you! I tested all n < 2,500,000 on "my" k so far and the last prime occured around n = 415,000. I hope I'll find at least one more prime until the end of the sieve at n = 4,100,000.
