files / problems / landau-n2-plus-1 / compute / q3 / n2p1.json

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{
  "n_max": 100000000,
  "count_prime": 3954181,
  "count_p2_omega_eq_2_composite": 12172983,
  "count_iwaniec_p2": 16127164,
  "count_omega_le2_composite_diagnostic": 12914417,
  "unsplit": 0,
  "omega_hist": {
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    "9": 13352,
    "10": 2346,
    "11": 355,
    "12": 64,
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  "C_q_truncated_product": 1.3727410102495463,
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    {
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      "pi_q": 3954181,
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  "seconds_roots": 2.317769224,
  "seconds_sieve_classify": 144.940052935,
  "rss_kb": 95520,
  "producer": "sieve_n2p1.c",
  "note": "prime_n: n=1 and even n with n^2+1 prime by deterministic MR (bases 2,3,5,7,11,13,17,19,23; OEIS A014233). Iwaniec P2 means \u03a9(n^2+1)<=2 (multiplicity). n^2+1 is never a square for n>=1, so \u03a9=2 means a product of two primes. P2 list is complete on 1<=n<=n_max. Not a proof of infinitude. Did not beat Wolf/Grantham published complete lists.",
  "prime_n_txt": "prime_n.txt",
  "p2_txt": "p2_omega2.txt",
  "prime_n_sha256": "ab3ea9a1215a6fd95dec7c1065712d1f2786870ebdc94bc587ff06a4dfee158b",
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  "verify_ok": "verify_ok.json"
}