Question

Are all numbers in this sequence prime numbers?\[a_1 = 2\]\[a_n = 2*a_{n-1} + 1\]

Answer 1

nope: the sixth number is 75

Answer 2

95 I mean :-P

Answer 3

fun fact: the 1000th number in this sequence is 16072629107794009814226375735900027158421072175583004111656255825555265766874041837397975682235437871913920093763297202377807179285384710653976866362047862205901851662236346478131611907593556712816931273229569712475372911901098151338748315919115594371856794716529813251490644747478936580255808502104063

Answer 4

there is no known formulation for the sequence of prime numbers. such a discovery would be one of the greatest in mathematics.

Answer 5

What about this, is the number \(S(x)=x^2+x+41\) prime for all non-negative integers x?

Answer 6

Who can find a counter example that shows what @TurningTest says about S(x)?

Answer 7

one moment @AnwarA :-D

Answer 8

There must be a good approach to this problem but I can't think of one and am just looking for a number by trial and error.

Answer 9

Trial and error works!

Answer 10

eventually...

Answer 11

Evaluate it at x=40.

Answer 12

Trial and error is the way to go

Answer 13

@TuringTest, the sequence doesn't claim to cover all primes.

Answer 14

0 41 True
1 43 True
2 47 True
3 53 True
4 61 True
5 71 True
6 83 True
7 97 True
8 113 True
9 131 True
10 151 True
11 173 True
12 197 True
13 223 True
14 251 True
15 281 True
16 313 True
17 347 True
18 383 True
19 421 True
20 461 True
21 503 True
22 547 True
23 593 True
24 641 True
25 691 True
26 743 True
27 797 True
28 853 True
29 911 True
30 971 True
31 1033 True
32 1097 True
33 1163 True
34 1231 True
35 1301 True
36 1373 True
37 1447 True
38 1523 True
39 1601 True
40 1681 False
41 1763 False
42 1847 True
43 1933 True
44 2021 False
45 2111 True
46 2203 True
47 2297 True
48 2393 True
49 2491 False
50 2591 True
51 2693 True
52 2797 True
53 2903 True
54 3011 True
55 3121 True
56 3233 False
57 3347 True
58 3463 True
59 3581 True
60 3701 True
61 3823 True
62 3947 True
63 4073 True
64 4201 True
65 4331 False
66 4463 True
67 4597 True
68 4733 True
69 4871 True
70 5011 True
71 5153 True
72 5297 True
73 5443 True
74 5591 True
75 5741 True
76 5893 False
77 6047 True
78 6203 True
79 6361 True
80 6521 True
81 6683 False
82 6847 False
83 7013 True
84 7181 False
85 7351 True
86 7523 True
87 7697 False
88 7873 True
89 8051 False
90 8231 True
91 8413 False
92 8597 True
93 8783 True
94 8971 True
95 9161 True
96 9353 False
97 9547 True
98 9743 True
99 9941 True

Answer 15

Where 'True' or 'False' is just saying whether that number in the middle is prime or not

Answer 16

I couldn't go that fast I guess. Cool formula, but I wish there was a better way to find where it fails.

Answer 17

So, x=40 is the first counter example. Nice!

Answer 18

did you use a program for that @adgd?

Answer 19

@TuringTest, if you want to find a neat way rather than trial and error, find the nth term for this sequence. From then it is clear why it is not always prime.