files / problems / landau-n2-plus-1 / compute / n2p1.json
{
"n_max": 1000000,
"count_prime": 54110,
"count_p2_omega_eq_2_composite": 147612,
"count_iwaniec_p2": 201722,
"count_omega_le2_composite_diagnostic": 158367,
"unsplit": 0,
"omega_hist": {
"1": 54110,
"2": 147612,
"3": 161065,
"4": 94019,
"5": 33209,
"6": 8151,
"7": 1541,
"8": 242,
"9": 44,
"10": 8
},
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1,
2,
4,
6,
10,
14,
16,
20,
24,
26,
36,
40,
54,
56,
66,
74,
84,
90,
94,
110,
116,
120,
124,
126,
130,
134,
146,
150,
156,
160
],
"first_prime_values": [
2,
5,
17,
37,
101,
197,
257,
401,
577,
677,
1297,
1601,
2917,
3137,
4357,
5477,
7057,
8101,
8837,
12101,
13457,
14401,
15377,
15877,
16901,
17957,
21317,
22501,
24337,
25601
],
"last_prime_n": [
999814,
999836,
999866,
999924,
999934,
999946,
999950,
999960
],
"last_prime_values": [
999628034597,
999672026897,
999732017957,
999848005777,
999868004357,
999892002917,
999900002501,
999920001601
],
"first_p2_n": [
8,
12,
22,
28,
30,
34,
42,
44,
46,
48,
50,
52
],
"C_q_published": 1.372813462818246,
"C_q_truncated_product": 1.3728105097807555,
"bateman_horn_integral": 39313.314489458324,
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"wolf_li_prediction": 53970.54997168725,
"prime_over_bh": 1.0025968685778837,
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"iwaniec_shape_N_over_logN_3_2": 19473.75004719696,
"wolf_A083844": [
{
"x": 1000000,
"pi_q": 112,
"wolf": 112,
"match": true
},
{
"x": 10000000,
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"match": true
},
{
"x": 100000000,
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},
{
"x": 1000000000,
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"match": true
},
{
"x": 10000000000,
"pi_q": 6656,
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},
{
"x": 100000000000,
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},
{
"x": 1000000000000,
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],
"seconds_sieve": 1.4522094989952166,
"seconds_classify": 35.41847860100097,
"note": "prime_n: n=1 and even n with n^2+1 prime by 64-bit MR. 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": "89b7f94046012758cbc48f0b1b4511efb2e864cae0a46b29ea7210317aa3bc32",
"p2_sha256": "9f3183d98bc58f09d5e48bf567f46fd6b39eb7cd710d4e81ca428aaf3cb49115",
"comparison_rows": [
{
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{
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{
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{
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}
]
}