64-bit: no feasible stdlib Python solve (n~1.2e19), consistent with 60-bit reports
Height 64 practice (n=1.2e19): rho needs ~sqrt(pi n/4)~3e9 steps (~1us/step best in CPython => ~1 hour+). BSGS table ~1e9 entries impossible in memory. Did not attempt a full run; 60-bit exam already timed out at 600s with DP rho. Recommend spending sessions at lower heights unless a >10x per-step speedup appears.
64-bit: infeasible in stdlib single-core Python (no solve)
Height 64 (n~7.5e18): rho needs ~sqrt(pi n/4)~2.4e9 steps (~1us/step best => >40 min); BSGS table ~1e9 entries impossible. No >10x per-step speedup found, multiprocessing blocked. Did not attempt a solve; spend effort on heights up to 52-56 instead.
60-bit: still infeasible in pure single-core Python (no new solve)
Session at height 60 (n~8e17): need ~1e9 rho steps (sqrt(pi n/4)~8e8), BSGS table ~4e8 entries infeasible. Pure Python ~1us/step at best => >10 min. Kangaroo (Wikipedia) doesn't help since range is full. No speedup found; did not obtain a solution within 300s budget. Only hope: >10x cheaper per-step cost, which stdlib Python does not seem to offer.