{
  "table": "T191",
  "baseline_revision": "52db67972f30a9fe16bd7622e45bd2b3c5f5b05c37026c7753161bc8f63fad57",
  "baseline_entries": 999,
  "status": "documented prime-counting benchmarks and offset constant",
  "selection": "it holds the offset-normalisation constant $\\operatorname{li}(2)$ and the prime-counting benchmarks $\\operatorname{li}(10^n)$ for $1\\leq n\\leq22$ from Table IV of CITE{PrimeCountingBenchmarks}; these are published application benchmarks, not an intrinsic preference for base ten",
  "reason": "The argument $2$ fixes the offset $\\operatorname{Li}(x)=\\operatorname{li}(x)-\\operatorname{li}(2)$. Table IV of CITE{PrimeCountingBenchmarks} compares $\\pi(x)$ with $\\operatorname{li}(x)$ at $x=10^n$, $1\\leq n\\leq22$. That explicit prime-counting use selects the benchmark arguments; their decimal form alone would not justify them. The values here use the unoffset principal-value convention CITE{formula-li}.",
  "primary_sources": [
    "https://sweet.ua.pt/tos/bib/5.4.pdf",
    "https://dlmf.nist.gov/6.2"
  ],
  "skill_sha256": "b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e809a7e06ded40b18",
  "earlier_skill_sha256": "ddda1bedfde5a883d9a3d1d24e88e731970776abd37e4a91d4c01c4af8542c44",
  "every_free_parameter": {
    "x": "documented prime-counting benchmarks and offset constant"
  },
  "retained_numeric_identifiers_reused_without_reassignment": true,
  "hand_edited_leaf_metadata_preserved": true,
  "removed_samples_retained_in_website_revision_history": true,
  "publication_or_approval_requested": false
}