Out of curiosity, I generated a 15360-bit candidate file.
On my laptop, it took 43 minutes to generate 3,264,148 prime candidates. The candidate file is 12 GB:
$ grep 'model name' /proc/cpuinfo | sort -u
model name : Intel(R) Core(TM) i7-8650U CPU @ 1.90GHz
$ wc -l 15360.candidates
3264148 15360.candidates
$ ls -l 15360.candidates
-rw-rw-r-- 1 aaron aaron 12658365944 Mar 2 13:54 15360.candidates
Currently screening the candidates for likely primes. Will report back later.