 |
Development of
Algorithmic Constructions |
01:46:12
|  | | | 19.Apr 2024
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Results for the primes distribution on quadratic polynomials
The following tables show a comparison between the primes distribution concerning quadratic irreducible polynomials.
The calculation for each polynomial needed appr. 22 hours on Amd Fx(tm) 6300, 2 Ghz, with 32GB Ram.
The green table indicates the amount of all primes concerning the n=2^exp for f(n)=an^2+bn+c.
The orange table compares the amount of the primes, where the primes p=f(n) are.
The yellow table lists up the amount of the reducible primes, where the primes p | f(n).
The 20 different polynomials are sorted by ascending order of the results and are
n²+1,
n²+n+1,
n²-2,
n²-3,
n²+2,
2n²-1,
2n²+1,
3n²-1,
4n²+1,
4n²+7,
4n²+3,
4n²-3,
4n²-5,
4n²-7,
4n²-11,
4n²-17,
4n²-23,
4n²-47,
4n²-83 and
4n²-167,
| A) all primes |
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| polynomial |
1,0,2 |
1,0,1 |
1,1,1 |
1,0,-3 |
1,0,-2 |
2,0,1 |
2,0,-1 |
4,0,-7 |
4,0,-11 |
4,0,-23 |
| exp |
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| 2 |
3 |
3 |
3 |
3 |
2 |
3 |
3 |
3 |
3 |
5 |
| 3 |
5 |
5 |
7 |
6 |
6 |
6 |
6 |
7 |
6 |
8 |
| 4 |
10 |
12 |
12 |
12 |
12 |
11 |
13 |
15 |
14 |
15 |
| 5 |
19 |
22 |
23 |
24 |
24 |
24 |
27 |
28 |
27 |
29 |
| 6 |
41 |
46 |
46 |
47 |
47 |
50 |
54 |
55 |
57 |
57 |
| 7 |
85 |
90 |
95 |
95 |
98 |
99 |
106 |
110 |
109 |
109 |
| 8 |
172 |
181 |
189 |
187 |
191 |
194 |
212 |
215 |
212 |
213 |
| 9 |
342 |
364 |
375 |
379 |
384 |
388 |
420 |
427 |
422 |
425 |
| 10 |
696 |
736 |
751 |
748 |
765 |
776 |
835 |
848 |
844 |
836 |
| 11 |
1.398 |
1.459 |
1.490 |
1.498 |
1.529 |
1.540 |
1.656 |
1.670 |
1.660 |
1.675 |
| 12 |
2.803 |
2.920 |
2.968 |
2.998 |
3.030 |
3.073 |
3.295 |
3.295 |
3.294 |
3.297 |
| 13 |
5.638 |
5.810 |
5.923 |
5.944 |
6.054 |
6.099 |
6.512 |
6.528 |
6.517 |
6.531 |
| 14 |
11.250 |
11.620 |
11.799 |
11.869 |
12.028 |
12.160 |
12.889 |
12.894 |
12.901 |
12.943 |
| 15 |
22.540 |
23.198 |
23.581 |
23.691 |
23.978 |
24.225 |
25.587 |
25.580 |
25.681 |
25.667 |
| 16 |
45.091 |
46.339 |
47.003 |
47.200 |
47.802 |
48.262 |
50.829 |
50.813 |
50.937 |
50.996 |
| 17 |
90.293 |
92.654 |
93.873 |
94.146 |
95.372 |
96.117 |
101.018 |
101.042 |
101.225 |
101.342 |
| 18 |
180.479 |
185.106 |
187.285 |
187.936 |
190.164 |
191.661 |
200.903 |
200.938 |
201.038 |
201.419 |
| 19 |
361.168 |
369.794 |
373.890 |
375.126 |
379.423 |
382.127 |
399.532 |
399.717 |
400.232 |
400.471 |
| 20 |
722.396 |
738.766 |
746.565 |
748.939 |
756.829 |
762.133 |
795.725 |
795.821 |
796.361 |
797.609 |
| 21 |
1.445.056 |
1.476.544 |
1.491.178 |
1.495.457 |
1.510.982 |
1.520.931 |
1.584.289 |
1.584.869 |
1.586.450 |
1.588.134 |
| 22 |
2.890.364 |
2.949.935 |
2.978.399 |
2.986.503 |
3.016.014 |
3.035.027 |
3.156.024 |
3.157.613 |
3.160.690 |
3.163.967 |
| 23 |
5.781.581 |
5.894.833 |
5.949.603 |
5.965.104 |
6.021.460 |
6.058.303 |
6.290.171 |
6.292.264 |
6.298.554 |
6.304.903 |
| 24 |
11.564.676 |
11.782.897 |
11.887.260 |
11.915.758 |
12.024.149 |
12.094.615 |
12.540.349 |
12.543.997 |
12.555.578 |
12.568.193 |
| 25 |
23.131.946 |
23.550.908 |
23.751.260 |
23.805.275 |
24.014.125 |
24.149.710 |
25.004.583 |
25.010.600 |
25.034.996 |
25.058.838 |
| 26 |
46.269.839 |
47.074.786 |
47.460.078 |
47.562.507 |
47.964.117 |
48.226.395 |
49.869.735 |
49.883.265 |
49.930.839 |
49.976.932 |
| 27 |
92.552.487 |
94.099.962 |
94.842.057 |
95.037.109 |
95.809.661 |
96.316.171 |
99.481.971 |
99.509.440 |
99.601.261 |
99.690.082 |
| 28 |
185.124.273 |
188.106.701 |
189.538.866 |
189.910.577 |
191.402.094 |
192.381.714 |
198.492.861 |
198.541.306 |
198.724.196 |
198.892.390 |
| 29 |
370.288.136 |
376.049.307 |
378.811.001 |
379.531.098 |
382.404.759 |
384.295.122 |
396.098.536 |
396.200.001 |
396.551.601 |
396.884.027 |
| 30 |
740.659.840 |
751.784.745 |
757.129.245 |
758.505.601 |
764.060.579 |
767.729.885 |
790.540.524 |
790.758.634 |
791.432.085 |
792.078.016 |
| 31 |
1.481.470.326 |
1.503.000.381 |
1.513.336.004 |
1.515.990.842 |
1.526.721.092 |
1.533.851.929 |
1.578.008.402 |
1.578.433.588 |
1.579.737.508 |
1.581.024.629 |
| 32 |
2.963.239.348 |
3.004.917.702 |
3.024.943.674 |
3.030.069.119 |
3.050.855.610 |
3.064.705.816 |
3.150.256.547 |
3.151.093.307 |
3.153.644.671 |
3.156.152.925 |
| 33 |
5.927.074.690 |
6.007.850.623 |
6.046.677.752 |
6.056.548.774 |
6.096.874.073 |
6.123.796.529 |
6.289.736.836 |
6.291.386.486 |
6.296.356.441 |
6.301.215.308 |
| 34 |
11.855.272.128 |
12.012.007.361 |
12.087.378.076 |
12.106.430.842 |
12.184.701.714 |
12.237.071.081 |
12.559.184.251 |
12.562.435.649 |
12.572.152.712 |
12.581.657.505 |
| 35 |
23.712.708.182 |
24.017.148.553 |
24.163.506.862 |
24.200.370.629 |
24.352.361.178 |
24.454.319.674 |
25.080.235.460 |
25.086.618.444 |
25.105.582.200 |
25.124.152.436 |
| 36 |
47.429.697.022 |
48.021.305.927 |
48.305.814.739 |
48.377.290.138 |
48.672.746.151 |
48.871.362.246 |
50.088.477.866 |
50.101.048.699 |
50.138.095.032 |
50.174.515.643 |
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| % |
69,019 |
69,880 |
70,294 |
70,398 |
70,828 |
71,117 |
72,888 |
72,907 |
72,961 |
73,014 |
| polynomial |
1,0,2 |
1,0,1 |
1,1,1 |
1,0,-3 |
1,0,-2 |
2,0,1 |
2,0,-1 |
4,0,-7 |
4,0,-11 |
4,0,-23 |
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| polynomial |
4,0,3 |
3,0,-1 |
4,0,1 |
4,0,-47 |
4,0,-3 |
4,0,-83 |
4,0,-5 |
4,0,7 |
4,0,-17 |
4,0,-167 |
| exp |
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| 2 |
5 |
4 |
4 |
5 |
4 |
5 |
3 |
4 |
4 |
5 |
| 3 |
8 |
8 |
8 |
9 |
8 |
9 |
8 |
9 |
8 |
9 |
| 4 |
16 |
14 |
15 |
16 |
15 |
17 |
16 |
17 |
16 |
17 |
| 5 |
30 |
30 |
30 |
31 |
31 |
32 |
30 |
32 |
32 |
33 |
| 6 |
56 |
57 |
58 |
59 |
57 |
62 |
61 |
63 |
63 |
64 |
| 7 |
109 |
112 |
112 |
111 |
114 |
120 |
119 |
119 |
120 |
127 |
| 8 |
214 |
221 |
220 |
219 |
225 |
231 |
231 |
233 |
237 |
249 |
| 9 |
424 |
432 |
441 |
429 |
443 |
447 |
449 |
455 |
465 |
482 |
| 10 |
842 |
850 |
855 |
852 |
872 |
882 |
879 |
899 |
911 |
937 |
| 11 |
1.664 |
1.675 |
1.679 |
1.684 |
1.720 |
1.729 |
1.735 |
1.758 |
1.802 |
1.827 |
| 12 |
3.299 |
3.334 |
3.323 |
3.344 |
3.400 |
3.413 |
3.433 |
3.452 |
3.540 |
3.595 |
| 13 |
6.537 |
6.580 |
6.595 |
6.623 |
6.723 |
6.753 |
6.762 |
6.820 |
6.982 |
7.054 |
| 14 |
12.936 |
13.082 |
13.045 |
13.131 |
13.287 |
13.370 |
13.398 |
13.536 |
13.787 |
13.882 |
| 15 |
25.672 |
25.931 |
25.880 |
26.015 |
26.285 |
26.446 |
26.572 |
26.755 |
27.321 |
27.393 |
| 16 |
51.003 |
51.461 |
51.435 |
51.616 |
52.106 |
52.472 |
52.663 |
52.971 |
54.015 |
54.278 |
| 17 |
101.341 |
102.114 |
102.141 |
102.510 |
103.426 |
104.221 |
104.445 |
105.122 |
107.023 |
107.574 |
| 18 |
201.576 |
203.046 |
203.029 |
203.654 |
205.577 |
206.900 |
207.386 |
208.669 |
212.322 |
213.240 |
| 19 |
401.002 |
403.642 |
403.734 |
405.040 |
408.620 |
411.321 |
412.049 |
414.547 |
421.192 |
423.278 |
| 20 |
797.999 |
803.205 |
803.573 |
805.850 |
812.723 |
817.940 |
819.192 |
824.004 |
836.671 |
840.497 |
| 21 |
1.588.883 |
1.599.166 |
1.599.253 |
1.604.041 |
1.617.355 |
1.627.326 |
1.629.246 |
1.638.814 |
1.663.016 |
1.670.302 |
| 22 |
3.165.689 |
3.184.835 |
3.184.946 |
3.194.393 |
3.219.208 |
3.238.915 |
3.242.571 |
3.260.809 |
3.307.330 |
3.321.348 |
| 23 |
6.308.880 |
6.344.114 |
6.344.870 |
6.363.292 |
6.411.421 |
6.448.641 |
6.454.833 |
6.490.074 |
6.579.246 |
6.606.829 |
| 24 |
12.575.653 |
12.642.924 |
12.645.628 |
12.680.778 |
12.771.707 |
12.844.241 |
12.854.590 |
12.922.710 |
13.094.883 |
13.147.967 |
| 25 |
25.074.793 |
25.201.398 |
25.207.257 |
25.276.219 |
25.449.873 |
25.588.497 |
25.609.577 |
25.741.119 |
26.072.283 |
26.176.348 |
| 26 |
50.007.482 |
50.250.380 |
50.260.969 |
50.394.228 |
50.726.504 |
50.996.776 |
51.036.159 |
51.286.059 |
51.927.217 |
52.127.620 |
| 27 |
99.748.052 |
100.216.532 |
100.239.238 |
100.496.607 |
101.133.746 |
101.662.456 |
101.734.027 |
102.213.707 |
103.448.953 |
103.839.529 |
| 28 |
199.002.178 |
199.907.149 |
199.958.544 |
200.452.614 |
201.684.694 |
202.702.560 |
202.837.241 |
203.763.008 |
206.149.113 |
206.909.938 |
| 29 |
397.093.379 |
398.839.619 |
398.940.000 |
399.896.951 |
402.266.988 |
404.251.662 |
404.503.680 |
406.287.104 |
410.905.017 |
412.378.643 |
| 30 |
792.479.799 |
795.850.386 |
796.054.419 |
797.917.700 |
802.496.368 |
806.348.029 |
806.821.706 |
810.273.902 |
819.213.163 |
822.078.899 |
| 31 |
1.581.788.144 |
1.588.300.505 |
1.588.702.041 |
1.592.330.017 |
1.601.166.576 |
1.608.675.449 |
1.609.552.031 |
1.616.256.570 |
1.633.560.988 |
1.639.134.427 |
| 32 |
3.157.630.501 |
3.170.234.432 |
3.171.017.355 |
3.178.084.343 |
3.195.185.584 |
3.209.781.369 |
3.211.451.397 |
3.224.449.993 |
3.257.997.170 |
3.268.851.282 |
| 33 |
6.304.072.980 |
6.328.491.928 |
6.330.108.091 |
6.343.865.835 |
6.376.943.869 |
6.405.374.461 |
6.408.542.286 |
6.433.739.198 |
6.498.843.170 |
6.520.003.012 |
| 34 |
12.587.179.528 |
12.634.502.563 |
12.637.730.074 |
12.664.573.737 |
12.728.650.103 |
12.784.038.830 |
12.790.016.318 |
12.839.012.345 |
12.965.493.123 |
13.006.701.306 |
| 35 |
25.134.864.491 |
25.226.655.904 |
25.233.098.862 |
25.285.433.390 |
25.409.798.383 |
25.517.762.477 |
25.529.090.788 |
25.624.369.300 |
25.870.226.911 |
25.950.601.945 |
| 36 |
50.195.124.246 |
50.373.401.462 |
50.386.282.403 |
50.488.391.823 |
50.729.881.676 |
50.940.422.045 |
50.962.013.019 |
51.147.447.597 |
51.625.772.531 |
51.782.673.936 |
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| % |
73,044 |
73,303 |
73,322 |
73,470 |
73,822 |
74,128 |
74,159 |
74,429 |
75,125 |
75,354 |
| polynomial |
4,0,3 |
3,0,-1 |
4,0,1 |
4,0,-47 |
4,0,-3 |
4,0,-83 |
4,0,-5 |
4,0,7 |
4,0,-17 |
4,0,-167 |
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| B) number of primes p = f(x) |
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| polynomial |
1,0,2 |
1,0,1 |
1,0,-3 |
2,0,1 |
4,0,-7 |
1,0,-2 |
3,0,-1 |
4,0,3 |
4,0,-11 |
1,1,1 |
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|
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| 2 |
3 |
3 |
3 |
2 |
2 |
2 |
3 |
4 |
3 |
3 |
| 3 |
3 |
4 |
4 |
3 |
4 |
4 |
5 |
6 |
4 |
6 |
| 4 |
5 |
7 |
6 |
4 |
6 |
7 |
7 |
8 |
9 |
9 |
| 5 |
6 |
10 |
9 |
8 |
10 |
11 |
12 |
13 |
14 |
14 |
| 6 |
10 |
14 |
15 |
12 |
14 |
20 |
21 |
21 |
20 |
22 |
| 7 |
16 |
24 |
26 |
22 |
27 |
32 |
31 |
36 |
35 |
38 |
| 8 |
24 |
43 |
41 |
37 |
43 |
53 |
52 |
61 |
68 |
66 |
| 9 |
43 |
70 |
69 |
70 |
69 |
96 |
92 |
112 |
106 |
108 |
| 10 |
70 |
114 |
123 |
120 |
119 |
161 |
163 |
186 |
181 |
196 |
| 11 |
113 |
212 |
218 |
223 |
209 |
289 |
297 |
332 |
337 |
352 |
| 12 |
200 |
393 |
389 |
392 |
369 |
544 |
534 |
593 |
608 |
654 |
| 13 |
367 |
713 |
713 |
714 |
710 |
961 |
1.016 |
1.095 |
1.094 |
1.174 |
| 14 |
691 |
1.301 |
1.304 |
1.293 |
1.334 |
1.792 |
1.844 |
2.003 |
2.048 |
2.167 |
| 15 |
1.262 |
2.459 |
2.421 |
2.372 |
2.462 |
3.331 |
3.436 |
3.708 |
3.729 |
3.951 |
| 16 |
2.347 |
4.615 |
4.515 |
4.484 |
4.665 |
6.081 |
6.429 |
6.923 |
7.056 |
7.364 |
| 17 |
4.375 |
8.418 |
8.562 |
8.450 |
8.722 |
11.387 |
12.128 |
12.955 |
13.227 |
13.780 |
| 18 |
8.233 |
15.867 |
15.995 |
15.902 |
16.494 |
21.317 |
22.774 |
24.325 |
25.001 |
25.776 |
| 19 |
15.452 |
29.843 |
30.069 |
29.956 |
31.146 |
40.220 |
43.168 |
46.079 |
47.134 |
48.561 |
| 20 |
29.173 |
56.534 |
57.009 |
57.002 |
59.048 |
76.224 |
81.646 |
87.391 |
89.572 |
91.980 |
| 21 |
55.369 |
106.787 |
107.840 |
108.191 |
112.129 |
144.181 |
154.864 |
166.330 |
169.873 |
174.691 |
| 22 |
105.583 |
203.025 |
204.655 |
205.398 |
213.613 |
274.311 |
295.090 |
316.791 |
324.453 |
331.924 |
| 23 |
201.200 |
387.308 |
390.252 |
392.498 |
407.899 |
522.317 |
563.613 |
604.139 |
618.971 |
632.763 |
| 24 |
384.217 |
739.671 |
745.708 |
751.210 |
781.349 |
998.286 |
1.079.146 |
1.156.462 |
1.185.367 |
1.208.189 |
| 25 |
735.830 |
1.416.635 |
1.427.090 |
1.439.421 |
1.499.295 |
1.910.299 |
2.070.945 |
2.217.692 |
2.273.083 |
2.314.216 |
| 26 |
1.411.281 |
2.716.922 |
2.736.167 |
2.764.920 |
2.880.603 |
3.660.832 |
3.977.787 |
4.260.832 |
4.365.931 |
4.435.345 |
| 27 |
2.711.808 |
5.218.926 |
5.257.030 |
5.316.867 |
5.543.808 |
7.032.024 |
7.650.457 |
8.196.850 |
8.398.617 |
8.521.876 |
| 28 |
5.216.839 |
10.044.585 |
10.119.280 |
10.237.140 |
10.680.856 |
13.530.333 |
14.740.867 |
15.797.355 |
16.183.499 |
16.398.035 |
| 29 |
10.052.115 |
19.352.155 |
19.500.520 |
19.746.417 |
20.604.026 |
26.076.182 |
28.430.816 |
30.484.076 |
31.225.726 |
31.594.046 |
| 30 |
19.394.575 |
37.339.024 |
37.631.611 |
38.119.892 |
39.806.231 |
50.322.316 |
54.917.488 |
58.895.058 |
60.332.876 |
60.971.160 |
| 31 |
37.469.705 |
72.139.395 |
72.702.752 |
73.682.997 |
76.987.239 |
97.225.942 |
106.193.920 |
113.919.267 |
116.691.004 |
117.790.467 |
| 32 |
72.477.480 |
139.535.723 |
140.612.644 |
142.607.233 |
149.059.574 |
188.053.712 |
205.567.014 |
220.584.774 |
225.937.944 |
227.834.670 |
| 33 |
140.336.836 |
270.187.320 |
272.278.713 |
276.272.479 |
288.908.247 |
364.114.624 |
398.353.307 |
427.568.513 |
437.939.941 |
441.146.458 |
| 34 |
272.010.741 |
523.695.185 |
527.737.486 |
535.760.398 |
560.528.462 |
705.755.392 |
772.719.076 |
829.514.811 |
849.639.960 |
855.066.149 |
| 35 |
527.736.039 |
1.016.029.276 |
1.023.919.349 |
1.039.909.544 |
1.088.474.832 |
1.369.222.759 |
1.500.270.038 |
1.610.743.023 |
1.649.863.571 |
1.658.944.367 |
| 36 |
1.024.827.760 |
1.973.029.796 |
1.988.288.899 |
2.020.283.544 |
2.115.510.924 |
2.658.892.853 |
2.915.290.716 |
3.130.555.622 |
3.206.591.909 |
3.221.420.579 |
|
|
|
|
|
|
|
|
|
|
|
| % |
1,491 |
2,871 |
2,893 |
2,940 |
3,078 |
3,869 |
4,242 |
4,556 |
4,666 |
4,688 |
| polynomial |
1,0,2 |
1,0,1 |
1,0,-3 |
2,0,1 |
4,0,-7 |
1,0,-2 |
3,0,-1 |
4,0,3 |
4,0,-11 |
1,1,1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| polynomial |
4,0,1 |
4,0,-3 |
4,0,-23 |
4,0,-47 |
4,0,-5 |
2,0,-1 |
4,0,7 |
4,0,-83 |
4,0,-17 |
4,0,-167 |
|
|
|
|
|
|
|
|
|
|
|
| 2 |
3 |
3 |
5 |
5 |
3 |
3 |
4 |
5 |
4 |
5 |
| 3 |
6 |
5 |
7 |
8 |
7 |
6 |
8 |
9 |
8 |
9 |
| 4 |
9 |
8 |
11 |
12 |
10 |
10 |
13 |
15 |
13 |
17 |
| 5 |
13 |
14 |
17 |
21 |
19 |
17 |
22 |
24 |
24 |
29 |
| 6 |
23 |
25 |
23 |
30 |
28 |
34 |
35 |
38 |
40 |
48 |
| 7 |
42 |
40 |
42 |
54 |
49 |
55 |
59 |
67 |
74 |
81 |
| 8 |
69 |
68 |
75 |
95 |
86 |
99 |
102 |
111 |
117 |
141 |
| 9 |
113 |
122 |
131 |
165 |
154 |
178 |
173 |
201 |
211 |
242 |
| 10 |
211 |
217 |
234 |
281 |
290 |
309 |
309 |
337 |
386 |
429 |
| 11 |
392 |
388 |
404 |
518 |
506 |
545 |
567 |
622 |
690 |
784 |
| 12 |
712 |
712 |
719 |
913 |
924 |
1.002 |
1.032 |
1.118 |
1.258 |
1.394 |
| 13 |
1.300 |
1.303 |
1.325 |
1.687 |
1.706 |
1.838 |
1.891 |
2.049 |
2.296 |
2.584 |
| 14 |
2.458 |
2.420 |
2.433 |
3.130 |
3.154 |
3.376 |
3.480 |
3.805 |
4.224 |
4.801 |
| 15 |
4.614 |
4.514 |
4.552 |
5.852 |
5.863 |
6.294 |
6.515 |
7.117 |
7.741 |
8.960 |
| 16 |
8.417 |
8.561 |
8.522 |
10.873 |
10.937 |
11.743 |
12.179 |
13.341 |
14.474 |
16.639 |
| 17 |
15.866 |
15.994 |
16.039 |
20.460 |
20.534 |
21.965 |
22.827 |
24.983 |
27.143 |
31.130 |
| 18 |
29.842 |
30.068 |
30.095 |
38.476 |
38.575 |
41.386 |
42.915 |
46.990 |
51.306 |
58.793 |
| 19 |
56.533 |
57.008 |
56.980 |
72.607 |
72.869 |
78.131 |
81.093 |
88.622 |
97.142 |
111.075 |
| 20 |
106.786 |
107.839 |
107.862 |
138.183 |
137.879 |
147.640 |
153.631 |
167.781 |
184.140 |
210.763 |
| 21 |
203.024 |
204.654 |
205.246 |
262.929 |
262.091 |
280.678 |
292.250 |
318.605 |
349.542 |
400.469 |
| 22 |
387.307 |
390.251 |
391.674 |
500.905 |
499.670 |
534.268 |
556.998 |
606.475 |
666.039 |
764.357 |
| 23 |
739.670 |
745.707 |
748.810 |
956.424 |
955.212 |
1.019.557 |
1.062.787 |
1.159.141 |
1.271.430 |
1.459.722 |
| 24 |
1.416.634 |
1.427.089 |
1.432.771 |
1.830.234 |
1.829.838 |
1.948.488 |
2.034.808 |
2.217.900 |
2.435.051 |
2.794.663 |
| 25 |
2.716.921 |
2.736.166 |
2.747.185 |
3.508.475 |
3.509.154 |
3.737.250 |
3.902.514 |
4.256.405 |
4.671.571 |
5.356.108 |
| 26 |
5.218.925 |
5.257.029 |
5.278.614 |
6.736.637 |
6.741.404 |
7.174.585 |
7.500.336 |
8.178.047 |
8.976.524 |
10.293.079 |
| 27 |
10.044.584 |
10.119.279 |
10.160.114 |
12.963.009 |
12.972.869 |
13.795.167 |
14.433.731 |
15.736.753 |
17.275.163 |
19.803.717 |
| 28 |
19.352.154 |
19.500.519 |
19.580.674 |
24.976.032 |
24.996.458 |
26.560.180 |
27.811.562 |
30.322.196 |
33.280.331 |
38.166.100 |
| 29 |
37.339.023 |
37.631.610 |
37.784.270 |
48.200.357 |
48.229.174 |
51.221.836 |
53.666.769 |
58.510.732 |
64.212.648 |
73.640.619 |
| 30 |
72.139.394 |
72.702.751 |
72.992.229 |
93.112.140 |
93.180.655 |
98.900.070 |
103.679.456 |
113.037.769 |
124.047.079 |
142.262.410 |
| 31 |
139.535.722 |
140.612.643 |
141.186.108 |
180.098.212 |
180.231.460 |
191.194.071 |
200.537.328 |
218.621.063 |
239.923.211 |
275.166.582 |
| 32 |
270.187.319 |
272.278.712 |
273.395.448 |
348.729.736 |
348.986.804 |
370.016.238 |
388.301.357 |
423.306.751 |
464.550.368 |
532.820.385 |
| 33 |
523.695.184 |
527.737.485 |
529.936.294 |
675.895.401 |
676.442.080 |
716.818.946 |
752.660.290 |
820.502.106 |
900.460.300 |
1.032.745.328 |
| 34 |
1.016.029.275 |
1.023.919.348 |
1.028.133.232 |
1.311.294.535 |
1.312.430.148 |
1.390.087.477 |
1.460.269.751 |
1.591.926.069 |
1.747.018.929 |
2.003.661.816 |
| 35 |
1.973.029.795 |
1.988.288.901 |
1.996.517.590 |
2.546.402.972 |
2.548.608.648 |
2.698.149.317 |
2.835.656.550 |
3.091.337.585 |
3.392.491.862 |
3.890.891.708 |
| 36 |
3.834.641.364 |
3.864.234.723 |
3.880.275.267 |
4.948.990.064 |
4.953.320.857 |
5.241.732.604 |
5.511.218.029 |
6.008.035.844 |
6.593.441.517 |
7.562.122.881 |
|
|
|
|
|
|
|
|
|
|
|
| % |
5,580 |
5,623 |
5,647 |
7,202 |
7,208 |
7,628 |
8,020 |
8,743 |
9,595 |
11,004 |
| polynomial |
4,0,1 |
4,0,-3 |
4,0,-23 |
4,0,-47 |
4,0,-5 |
2,0,-1 |
4,0,7 |
4,0,-83 |
4,0,-17 |
4,0,-167 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| C) number of primes p | f(x) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| polynomial |
4,0,-167 |
2,0,-1 |
4,0,-83 |
4,0,-17 |
1,1,1 |
4,0,-47 |
4,0,7 |
4,0,-5 |
1,0,-2 |
1,0,1 |
|
|
|
|
|
|
|
|
|
|
|
| 2 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 3 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
2 |
1 |
| 4 |
0 |
3 |
2 |
3 |
3 |
4 |
4 |
6 |
5 |
5 |
| 5 |
4 |
10 |
8 |
8 |
9 |
10 |
10 |
11 |
13 |
12 |
| 6 |
16 |
20 |
24 |
23 |
24 |
29 |
28 |
33 |
27 |
32 |
| 7 |
46 |
51 |
53 |
46 |
57 |
57 |
60 |
70 |
66 |
66 |
| 8 |
108 |
113 |
120 |
120 |
123 |
124 |
131 |
145 |
138 |
138 |
| 9 |
240 |
242 |
246 |
254 |
267 |
264 |
282 |
295 |
288 |
294 |
| 10 |
508 |
526 |
545 |
525 |
555 |
571 |
590 |
589 |
604 |
622 |
| 11 |
1.043 |
1.111 |
1.107 |
1.112 |
1.138 |
1.166 |
1.191 |
1.229 |
1.240 |
1.247 |
| 12 |
2.201 |
2.293 |
2.295 |
2.282 |
2.314 |
2.431 |
2.420 |
2.509 |
2.486 |
2.527 |
| 13 |
4.470 |
4.674 |
4.704 |
4.686 |
4.749 |
4.936 |
4.929 |
5.056 |
5.093 |
5.097 |
| 14 |
9.081 |
9.513 |
9.565 |
9.563 |
9.632 |
10.001 |
10.056 |
10.244 |
10.236 |
10.319 |
| 15 |
18.433 |
19.293 |
19.329 |
19.580 |
19.630 |
20.163 |
20.240 |
20.709 |
20.647 |
20.739 |
| 16 |
37.639 |
39.086 |
39.131 |
39.541 |
39.639 |
40.743 |
40.792 |
41.726 |
41.721 |
41.724 |
| 17 |
76.444 |
79.053 |
79.238 |
79.880 |
80.093 |
82.050 |
82.295 |
83.911 |
83.985 |
84.236 |
| 18 |
154.447 |
159.517 |
159.910 |
161.016 |
161.509 |
165.178 |
165.754 |
168.811 |
168.847 |
169.239 |
| 19 |
312.203 |
321.401 |
322.699 |
324.050 |
325.329 |
332.433 |
333.454 |
339.180 |
339.203 |
339.951 |
| 20 |
629.734 |
648.085 |
650.159 |
652.531 |
654.585 |
667.667 |
670.373 |
681.313 |
680.605 |
682.232 |
| 21 |
1.269.833 |
1.303.611 |
1.308.721 |
1.313.474 |
1.316.487 |
1.341.112 |
1.346.564 |
1.367.155 |
1.366.801 |
1.369.757 |
| 22 |
2.556.991 |
2.621.756 |
2.632.440 |
2.641.291 |
2.646.475 |
2.693.488 |
2.703.811 |
2.742.901 |
2.741.703 |
2.746.910 |
| 23 |
5.147.107 |
5.270.614 |
5.289.500 |
5.307.816 |
5.316.840 |
5.406.868 |
5.427.287 |
5.499.621 |
5.499.143 |
5.507.525 |
| 24 |
10.353.304 |
10.591.861 |
10.626.341 |
10.659.832 |
10.679.071 |
10.850.544 |
10.887.902 |
11.024.752 |
11.025.863 |
11.043.226 |
| 25 |
20.820.240 |
21.267.333 |
21.332.092 |
21.400.712 |
21.437.044 |
21.767.744 |
21.838.605 |
22.100.423 |
22.103.826 |
22.134.273 |
| 26 |
41.834.541 |
42.695.150 |
42.818.729 |
42.950.693 |
43.024.733 |
43.657.591 |
43.785.723 |
44.294.755 |
44.303.285 |
44.357.864 |
| 27 |
84.035.812 |
85.686.804 |
85.925.703 |
86.173.790 |
86.320.181 |
87.533.598 |
87.779.976 |
88.761.158 |
88.777.637 |
88.881.036 |
| 28 |
168.743.838 |
171.932.681 |
172.380.364 |
172.868.782 |
173.140.831 |
175.476.582 |
175.951.446 |
177.840.783 |
177.871.761 |
178.062.116 |
| 29 |
338.738.024 |
344.876.700 |
345.740.930 |
346.692.369 |
347.216.955 |
351.696.594 |
352.620.335 |
356.274.506 |
356.328.577 |
356.697.152 |
| 30 |
679.816.489 |
691.640.454 |
693.310.260 |
695.166.084 |
696.158.085 |
704.805.560 |
706.594.446 |
713.641.051 |
713.738.263 |
714.445.721 |
| 31 |
1.363.967.845 |
1.386.814.331 |
1.390.054.386 |
1.393.637.777 |
1.395.545.537 |
1.412.231.805 |
1.415.719.242 |
1.429.320.571 |
1.429.495.150 |
1.430.860.986 |
| 32 |
2.736.030.897 |
2.780.240.309 |
2.786.474.618 |
2.793.446.802 |
2.797.109.004 |
2.829.354.607 |
2.836.148.636 |
2.862.464.593 |
2.862.801.898 |
2.865.381.979 |
| 33 |
5.487.257.684 |
5.572.917.890 |
5.584.872.355 |
5.598.382.870 |
5.605.531.294 |
5.667.970.434 |
5.681.078.908 |
5.732.100.206 |
5.732.759.449 |
5.737.663.303 |
| 34 |
11.003.039.490 |
11.169.096.774 |
11.192.112.761 |
11.218.474.194 |
11.232.311.927 |
11.353.279.202 |
11.378.742.594 |
11.477.586.170 |
11.478.946.322 |
11.488.312.176 |
| 35 |
22.059.710.237 |
22.382.086.143 |
22.426.424.892 |
22.477.735.049 |
22.504.562.495 |
22.739.030.418 |
22.788.712.750 |
22.980.482.140 |
22.983.138.419 |
23.001.119.277 |
| 36 |
44.220.551.055 |
44.846.745.262 |
44.932.386.201 |
45.032.331.014 |
45.084.394.160 |
45.539.401.759 |
45.636.229.568 |
46.008.692.162 |
46.013.853.298 |
46.048.276.131 |
|
|
|
|
|
|
|
|
|
|
|
| % |
64,349 |
65,261 |
65,385 |
65,531 |
65,606 |
66,269 |
66,409 |
66,951 |
66,959 |
67,009 |
| polynomial |
4,0,-167 |
2,0,-1 |
4,0,-83 |
4,0,-17 |
1,1,1 |
4,0,-47 |
4,0,7 |
4,0,-5 |
1,0,-2 |
1,0,1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| polynomial |
4,0,-23 |
1,0,-3 |
1,0,2 |
4,0,1 |
2,0,1 |
4,0,-3 |
4,0,-11 |
4,0,3 |
3,0,-1 |
4,0,-7 |
|
|
|
|
|
|
|
|
|
|
|
| 2 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
| 3 |
1 |
2 |
2 |
2 |
3 |
3 |
2 |
2 |
3 |
3 |
| 4 |
4 |
6 |
5 |
6 |
7 |
7 |
5 |
8 |
7 |
9 |
| 5 |
12 |
15 |
13 |
17 |
16 |
17 |
13 |
17 |
18 |
18 |
| 6 |
34 |
32 |
31 |
35 |
38 |
32 |
37 |
35 |
36 |
41 |
| 7 |
67 |
69 |
69 |
70 |
77 |
74 |
74 |
73 |
81 |
83 |
| 8 |
138 |
146 |
148 |
151 |
157 |
157 |
144 |
153 |
169 |
172 |
| 9 |
294 |
310 |
299 |
328 |
318 |
321 |
316 |
312 |
340 |
358 |
| 10 |
602 |
625 |
626 |
644 |
656 |
655 |
663 |
656 |
687 |
729 |
| 11 |
1.271 |
1.280 |
1.285 |
1.287 |
1.317 |
1.332 |
1.323 |
1.332 |
1.378 |
1.461 |
| 12 |
2.578 |
2.609 |
2.603 |
2.611 |
2.681 |
2.688 |
2.686 |
2.706 |
2.800 |
2.926 |
| 13 |
5.206 |
5.231 |
5.271 |
5.295 |
5.385 |
5.420 |
5.423 |
5.442 |
5.564 |
5.818 |
| 14 |
10.510 |
10.565 |
10.559 |
10.587 |
10.867 |
10.867 |
10.853 |
10.933 |
11.238 |
11.560 |
| 15 |
21.115 |
21.270 |
21.278 |
21.266 |
21.853 |
21.771 |
21.952 |
21.964 |
22.495 |
23.118 |
| 16 |
42.474 |
42.685 |
42.744 |
43.018 |
43.778 |
43.545 |
43.881 |
44.080 |
45.032 |
46.148 |
| 17 |
85.303 |
85.584 |
85.918 |
86.275 |
87.667 |
87.432 |
87.998 |
88.386 |
89.986 |
92.320 |
| 18 |
171.324 |
171.941 |
172.246 |
173.187 |
175.759 |
175.509 |
176.037 |
177.251 |
180.272 |
184.444 |
| 19 |
343.491 |
345.057 |
345.716 |
347.201 |
352.171 |
351.612 |
353.098 |
354.923 |
360.474 |
368.571 |
| 20 |
689.747 |
691.930 |
693.223 |
696.787 |
705.131 |
704.884 |
706.789 |
710.608 |
721.559 |
736.773 |
| 21 |
1.382.888 |
1.387.617 |
1.389.687 |
1.396.229 |
1.412.740 |
1.412.701 |
1.416.577 |
1.422.553 |
1.444.302 |
1.472.740 |
| 22 |
2.772.293 |
2.781.848 |
2.784.781 |
2.797.639 |
2.829.629 |
2.828.957 |
2.836.237 |
2.848.898 |
2.889.745 |
2.944.000 |
| 23 |
5.556.093 |
5.574.852 |
5.580.381 |
5.605.200 |
5.665.805 |
5.665.714 |
5.679.583 |
5.704.741 |
5.780.501 |
5.884.365 |
| 24 |
11.135.422 |
11.170.050 |
11.180.459 |
11.228.994 |
11.343.405 |
11.344.618 |
11.370.211 |
11.419.191 |
11.563.778 |
11.762.648 |
| 25 |
22.311.653 |
22.378.185 |
22.396.116 |
22.490.336 |
22.710.289 |
22.713.707 |
22.761.913 |
22.857.101 |
23.130.453 |
23.511.305 |
| 26 |
44.698.318 |
44.826.340 |
44.858.558 |
45.042.044 |
45.461.475 |
45.469.475 |
45.564.908 |
45.746.650 |
46.272.593 |
47.002.662 |
| 27 |
89.529.968 |
89.780.079 |
89.840.679 |
90.194.654 |
90.999.304 |
91.014.467 |
91.202.644 |
91.551.202 |
92.566.075 |
93.965.632 |
| 28 |
179.311.716 |
179.791.297 |
179.907.434 |
180.606.390 |
182.144.574 |
182.184.175 |
182.540.697 |
183.204.823 |
185.166.282 |
187.860.450 |
| 29 |
359.099.757 |
360.030.578 |
360.236.021 |
361.600.977 |
364.548.705 |
364.635.378 |
365.325.875 |
366.609.303 |
370.408.803 |
375.595.975 |
| 30 |
719.085.787 |
720.873.990 |
721.265.265 |
723.915.025 |
729.609.993 |
729.793.617 |
731.099.209 |
733.584.741 |
740.932.898 |
750.952.403 |
| 31 |
1.439.838.521 |
1.443.288.090 |
1.444.000.621 |
1.449.166.319 |
1.460.168.932 |
1.460.553.933 |
1.463.046.504 |
1.467.868.877 |
1.482.106.585 |
1.501.446.349 |
| 32 |
2.882.757.477 |
2.889.456.475 |
2.890.761.868 |
2.900.830.036 |
2.922.098.583 |
2.922.906.872 |
2.927.706.727 |
2.937.045.727 |
2.964.667.418 |
3.002.033.733 |
| 33 |
5.771.279.014 |
5.784.270.061 |
5.786.737.854 |
5.806.412.907 |
5.847.524.050 |
5.849.206.384 |
5.858.416.500 |
5.876.504.467 |
5.930.138.621 |
6.002.478.239 |
| 34 |
11.553.524.273 |
11.578.693.356 |
11.583.261.387 |
11.621.700.799 |
11.701.310.683 |
11.704.730.755 |
11.722.512.752 |
11.757.664.717 |
11.861.783.487 |
12.001.907.187 |
| 35 |
23.127.634.846 |
23.176.451.280 |
23.184.972.143 |
23.260.069.067 |
23.414.410.130 |
23.421.509.482 |
23.455.718.629 |
23.524.121.468 |
23.726.385.866 |
23.998.143.612 |
| 36 |
46.294.240.376 |
46.389.001.239 |
46.404.869.262 |
46.551.641.039 |
46.851.078.702 |
46.865.646.953 |
46.931.503.123 |
47.064.568.624 |
47.458.110.746 |
47.985.537.775 |
|
|
|
|
|
|
|
|
|
|
|
| % |
67,367 |
67,505 |
67,528 |
67,742 |
68,177 |
68,198 |
68,294 |
68,488 |
69,061 |
69,828 |
| polynomial |
4,0,-23 |
1,0,-3 |
1,0,2 |
4,0,1 |
2,0,1 |
4,0,-3 |
4,0,-11 |
4,0,3 |
3,0,-1 |
4,0,-7 |
|