A Prime Sequence

davar55 · 2008-12-03, 20:26

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:

Originally Posted by CRGreathouse

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 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:

Originally Posted by grandpascorpion

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

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:

Originally Posted by grandpascorpion

13-bad : 1746334757
14-bad : 3170297129

(minimal primes this time)

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:

Originally Posted by grandpascorpion

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

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.

2008-12-03, 20:26	#1
davar55 May 2004 New York City 5×7×11² Posts	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)?

2008-12-04, 19:49	#3
CRGreathouse Aug 2006 5,987 Posts	1 5 2 47 3 389 4 449 5 26627 6 47681 7 237343 8 1108337 9 2875111 10 9189181 11 12180187 12 208564813 Last fiddled with by CRGreathouse on 2008-12-04 at 19:50

2008-12-05, 04:01	#5
CRGreathouse Aug 2006 5,987 Posts	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). Last fiddled with by CRGreathouse on 2008-12-05 at 04:26

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2008-12-04, 19:46	#2
grandpascorpion Jan 2005 Transdniestr 503₁₀ Posts	Isn't 2 the first 1-bad number?

2008-12-05, 05:46	#6
grandpascorpion Jan 2005 Transdniestr 767₈ Posts	Ah, right again. Back to the drawing board ...

2008-12-05, 15:32	#8
grandpascorpion Jan 2005 Transdniestr 503₁₀ Posts	13-bad : 1746334757 14-bad : 3170297129 (minimal primes this time)

2008-12-06, 06:05	#10
grandpascorpion Jan 2005 Transdniestr 503 Posts	By the way, I checked through 4 billion. No results for 15. I'm done for now anyways :)