files / problems / landau-n2-plus-1 / compute / q2 / n2p1.json

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{
  "n_max": 10000000,
  "count_prime": 456362,
  "count_p2_omega_eq_2_composite": 1334083,
  "count_iwaniec_p2": 1790445,
  "count_omega_le2_composite_diagnostic": 1421501,
  "unsplit": 0,
  "omega_hist": {
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    "2": 1334083,
    "3": 1590647,
    "4": 1041493,
    "5": 425651,
    "6": 120548,
    "7": 25585,
    "8": 4724,
    "9": 747,
    "10": 139,
    "11": 18,
    "12": 4
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  "first_prime_values": [
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  "last_prime_values": [
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  "first_p2_n": [
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    50,
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  "C_q_truncated_product": 1.3727410102495463,
  "bateman_horn_integral": 332462.8855200837,
  "bateman_horn_prediction": 456409.5251293722,
  "wolf_li_prediction": 456404.5400175865,
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  "prime_over_wolf_li": 0.9999067931761045,
  "iwaniec_shape_N_over_logN_3_2": 154535.90752835674,
  "wolf_A083844": [
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      "match": true
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    {
      "x": 10000000,
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    {
      "x": 100000000,
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    {
      "x": 1000000000,
      "pi_q": 2378,
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    },
    {
      "x": 10000000000,
      "pi_q": 6656,
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      "match": true
    },
    {
      "x": 100000000000,
      "pi_q": 18822,
      "wolf": 18822,
      "match": true
    },
    {
      "x": 1000000000000,
      "pi_q": 54110,
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    {
      "x": 10000000000000,
      "pi_q": 156081,
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      "match": true
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    {
      "x": 100000000000000,
      "pi_q": 456362,
      "wolf": 456362,
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  ],
  "seconds_sieve": 0.689969803,
  "seconds_classify": 14.064709393,
  "rss_kb": 55832,
  "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": "31207a4a146e862e3a55882a8395b94567d8cc49292a935df7624ac915011409",
  "p2_sha256": "aa7f83c18bbe68419888212bb6e1fe7b5787949e6084a553bdc9d03bbcd56f5a",
  "prime_n_bytes": 3589210,
  "p2_bytes": 31970643,
  "comparison_rows": [
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  "seconds_c_verify": 53.1,
  "seconds_python_verify": 885.18,
  "verify_ok": "verify_ok.json"
}