Problems & Puzzles: Puzzles

Puzzle 1139 prime producing IRREGULAR polynomials

This new puzzle correspond to the class of puzzles related with prime producing polynomials that we have studied in several pages in this site: Problem 12, and Puzzles 232, 782, 1097, 1099, 1135, more?

Because of the nature of this new polynomial I will name it "prime producing IRREGULAR polynomials"

The Davide Rotondo specific one goes like this:

abs(n^2 - 108n + 2518) produces 109 consecutive primes, n=0 to 108. But if n is even the result must be divided by 2 except when the result is 2.

From 0 to 55 for n=32 & 33 the function provides the same prime(43) and for n=35 & 36 the function provide the same prime (37).

From n=55 to n=108 the values repeat in reverse order. Accordingly for n=75 & 76 the function provide the same prime (43) and for n=72 & 73 the function provides the same prime (37).

In total, from the 109 primes only 53 are distinct.

Here are all the primes, for n=0 to 109

n Abs(n^2-108*n+2518)
0 1259
1 2411
2 1153
3 2203
4 1051
5 2003
6 953
7 1811
8 859
9 1627
10 769
11 1451
12 683
13 1283
14 601
15 1123
16 523
17 971
18 449
19 827
20 379
21 691
22 313
23 563
24 251
25 443
26 193
27 331
28 139
29 227
30 89
31 131
32 43
33 43 R
34 2
35 37
36 37 R
37 109
38 71
39 173
40 101
41 229
42 127
43 277
44 149
45 317
46 167
47 349
48 181
49 373
50 191
51 389
52 197
53 397

54 199 55th central prime

55 397 From this one all the prime are repeated
              in reverse order jumping over the central
              one
56 197
57 389
58 191
59 373
60 181
61 349
62 167
63 317
64 149
65 277
66 127
67 229
68 101
69 173
70 71
71 109
72 37
73 37
74 1
75 43
76 43
77 131
78 89
79 227
80 139
81 331
82 193
83 443
84 251
85 563
86 313
87 691
88 379
89 827
90 449
91 971
92 523
93 1123
94 601
95 1283
96 683
97 1451
98 769
99 1627
100 859
101 1811
102 953
103 2003
104 1051
105 2203
106 1153
107 2411
108 1259

Q. Can you send a better prime  producing
IRREGULAR polynomial?

 


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