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-   -   A Prime Sequence (https://www.mersenneforum.org/showthread.php?t=11081)

davar55 2008-12-03 20:26

A Prime Sequence
 
Call a prime p "d-nice" if there is another prime of the form ap +/- b,
with 1 <= a,b <= d.

What are the smallest primes that are NOT d-nice,
for d = 1,2,3,4,5 (etc)?

grandpascorpion 2008-12-04 19:46

Isn't 2 the first 1-bad number?

CRGreathouse 2008-12-04 19:49

1 5
2 47
3 389
4 449
5 26627
6 47681
7 237343
8 1108337
9 2875111
10 9189181
11 12180187
12 208564813

grandpascorpion 2008-12-04 22:28

[QUOTE=CRGreathouse;151984]1 5
2 47
3 389
4 449
5 26627
6 47681
7 237343
8 1108337
9 2875111
10 9189181
11 12180187
12 208564813[/QUOTE]

13 226936710 (first even minimum)

CRGreathouse 2008-12-05 04:01

The original question was about primes with this property, so 226936710 isn't the 13th solution. If we allowed composites then the 5th solution is 11850, not 26627 (and so on).

grandpascorpion 2008-12-05 05:46

Ah, right again. Back to the drawing board ...

CRGreathouse 2008-12-05 13:11

13 1746334757

[QUOTE=grandpascorpion;152032]Ah, right again. Back to the drawing board ...[/QUOTE]

It happens, don't worry about it. Maybe you can calculate this variant sequence? It seems to be at least as interesting as the original. Since you came up with it I'll let you have the first real whack at it. It should start like:

1 5
2 47
3 389
4 449
5 11850

(but check that, don't trust me!)

grandpascorpion 2008-12-05 15:32

13-bad : 1746334757
14-bad : 3170297129

(minimal primes this time)

CRGreathouse 2008-12-06 00:12

[QUOTE=grandpascorpion;152068]13-bad : 1746334757
14-bad : 3170297129

(minimal primes this time)[/QUOTE]

You beat me to 14! (Your result matches mine: my computer finished it, but I didn't see the result until after your post.) Good for you. I'm working on 15 now; since I only just started I imagine you'll win there, too.

grandpascorpion 2008-12-06 06:05

By the way, I checked through 4 billion. No results for 15. I'm done for now anyways :)

CRGreathouse 2008-12-06 15:38

[QUOTE=grandpascorpion;152173]By the way, I checked through 4 billion. No results for 15. I'm done for now anyways :)[/QUOTE]

Cool. I set my computer to search through 40 billion; I don't know how far it is through that process, but hopefully not more than a day away.

Jens K Andersen 2008-12-07 08:25

15-bad: 16434786721

Jens K Andersen 2008-12-08 04:43

16-bad: 51321114983
I stopped the search there.

CRGreathouse 2008-12-08 15:24

So here are the minimal k-bad primes for k in 1..16, in Sloane b-file format:

1 5
2 47
3 389
4 449
5 26627
6 47681
7 237343
8 1108337
9 2875111
10 9189181
11 12180187
12 208564813
13 1746334757
14 3170297129
15 16434786721
16 51321114983

davar55 2008-12-11 14:38

[quote=CRGreathouse;152482]So here are the minimal k-bad primes for k in 1..16, in Sloane b-file format:

1 5
2 47
3 389
4 449
5 26627
6 47681
7 237343
8 1108337
9 2875111
10 9189181
11 12180187
12 208564813
13 1746334757
14 3170297129
15 16434786721
16 51321114983[/quote]

Is this something that should be submitted to OEIS?

CRGreathouse 2008-12-11 15:56

[QUOTE=davar55;152900]Is this something that should be submitted to OEIS?[/QUOTE]

I didn't think so, but if you'd like to the format's all ready to go. :smile:

I'm trying for 17, but that hasn't gone anywhere yet. I won't have the patience or processing power to do 18.

davar55 2009-07-02 19:58

Have you tried, not a sieve, or a multi-core processor,
but strictly two processors running in parallel
and exchanging data and information ala by the internet?


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