[SethTro]

Is that for [0, 10^12] or for 10^18 + 10^12? Is the 3.75 hrs total core hours or system time?

I wrote https://github.com/sethtroisi/goldbach in the last four hours and I think it's 10-100x faster than your code

  time ./goldbach -t8 -K 1024 -e 100''000''000''000
  real 0m44.133s
  user 3m32.193s
  sys 0m0.092s

  time ./goldbach -t12 -K 1500 -e 1''000''000''000''000
    267468893942 = 267468891139 + 2803 (407)
    926868341768 = 926868338701 + 3067 (437)
    599533546358 = 599533542901 + 3457 (481)
  real 2m3.909s
  user 16m0.729s
  sys 0m37.960s

I know of at least another 4x I could improve it but I've been nerd sniped enough for the night.

I wouldn't trust it 100% but it finds all terms in https://oeis.org/A025018 and https://oeis.org/A025019 and I can verify in https://sweet.ua.pt/tos/goldbach.html