My 6x40 stage 1 run with B1=5e9 finished without finding a factor of 4^444 + 3. On to stage 2!

@Peter Very good. If we compare $\Phi_{15}$ with $\Phi_{24}$ then $\Phi_{24}$ obviously generates more primes in the same range, right?

@hardmath You mentioned to send you the residues from B1 results to then prepare fast B2 operations. Is this done with GMP-ECM 'save' option?

@Peter I have no idea why $k=-21$ generates more primes.

@MartinHopf Yes, I was running six stage 1 processes simultaneously, as these take comparatively little memory. The stage 2 process is faster (half an hour rather than 4.3 hours for stage 1), but requires almost all of my RAM. So that the stage 1 processes which took a little more than a week require a little less than a week to complete in stage 2.

I used the -save option in stage 1 and the -resume option of GMP-ECM in stage 2.

@hardmath OK. What is the proper command line input in GMP-ECM so one can get a 'save' file for you to process?

@MartinHopf Hi

We have $\varphi(15)=\varphi(24)=8$, so it is no surprise that $\phi_{24}$ produces more primes than $\phi_{15}$

@MartinHopf You are (IRC) on Windows, but the command line interface should be similar to this:

ecm -save fillename -c 40 5e9 1

Of course filename is a placeholder for whatever file name you want to use. The -c 40 causes the program to repeat forty times (may be too much for your patience), the 5e9 is the B1 parameter, and the trailing 1 sets B2 so low that stage 2 will not actually run.