数学家R.Ruby于1990年发现二次三项式f(x)=36x^2-810x+2753在X=0到44时,
可以得到45个连续素数。这是目前素数生成长度最大的二次三项式。
其中有14个负数,将它们变成正数,一起分解,这45个整数都是素数!
x=45的后面,还有较大的素数。
f(x)=36x^2-810x+2753
x f(x) f(x)绝对值 素性
0 2753 2753 prime
1 1979 1979 prime
2 1277 1277 prime
3 647 647 prime
4 89 89 prime
5 -397 397 prime
6 -811 811 prime
7 -1153 1153 prime
8 -1423 1423 prime
9 -1621 1621 prime
10 -1747 1747 prime
11 -1801 1801 prime
12 -1783 1783 prime
13 -1693 1693 prime
14 -1531 1531 prime
15 -1297 1297 prime
16 -991 991 prime
17 -613 613 prime
18 -163 163 prime
19 359 359 prime
20 953 953 prime
21 1619 1619 prime
22 2357 2357 prime
23 3167 3167 prime
24 4049 4049 prime
25 5003 5003 prime
26 6029 6029 prime
27 7127 7127 prime
28 8297 8297 prime
29 9539 9539 prime
30 10853 10853 prime
31 12239 12239 prime
32 13697 13697 prime
33 15227 15227 prime
34 16829 16829 prime
35 18503 18503 prime
36 20249 20249 prime
37 22067 22067 prime
38 23957 23957 prime
39 25919 25919 prime
40 27953 27953 prime
41 30059 30059 prime
42 32237 32237 prime
43 34487 34487 prime
44 36809 36809 prime
45 39203 39203=197*199
46 41669 41669 prime
47 44207 44207 prime
48 46817 46817 prime
49 49499 49499 prime
50 52253 52253 prime
51 55079 55079 prime
52 57977 57977 prime
53 60947 60947=59*1033
54 63989 63989=61*1049
55 67103 67103 prime
56 70289 70289 prime
57 73547 73547 prime
58 76877 76877=59*1303
59 80279 80279 prime
60 83753 83753=61*1373
61 87299 87299 prime
62 90917 90917 prime
63 94607 94607=89*1063
64 98369 98369 prime
65 102203 102203 prime
66 106109 106109 prime
向前后延伸,还有一些素数,但连续素数很少。
x f(x)
0 1853=17*109
1 1529=11*139
2 1277 is prime
3 1097 is prime
4 989=23*43
53 83897=11*29*263
54 87389=31*2819
55 90953=19*4787
56 94589=11*8599
57 98297 is prime
58 102077 is prime
59 105929 is prime
60 109853=37*2969
61 113849=17*37*181
62 117917 is prime
63 122057=13*41*229
64 126269=11*13*883
65 130553 is prime
66 134909 is prime
67 139337=11*53*239
68 143837=17*8461
69 148409=19*73*107
70 153053=41*3733
71 157769 is prime
72 162557 is prime
73 167417=23*29*251
74 172349=19*47*193
75 177353=11*23*701
76 182429=13*14033
77 187577=13*47*307
78 192797=11*17*1031
79 198089=113*1753
80 203453=31*6563
81 208889 is prime
82 214397=29*7393
83 219977 is prime
84 225629 is prime
85 231353=17*31*439
86 237149=11*21559
87 243017=73*3329
88 248957=19*13103
89 254969=11*13*1783
90 261053=13*43*467
91 267209=191*1399
92 273437=43*6359
93 279737=19*14723
94 286109=223*1283
95 292553=17*17209
96 299069=23*13003
97 305657=11*37*751
98 312317=23*37*367
99 319049 is prime
100 325853=11*11*2693