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 2008-12-03, 20:26 #1 davar55     May 2004 New York City 102138 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, 19:46 #2 grandpascorpion     Jan 2005 Transdniestr 50310 Posts Isn't 2 the first 1-bad number?
 2008-12-04, 19:49 #3 CRGreathouse     Aug 2006 3·1,993 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
2008-12-04, 22:28   #4
grandpascorpion

Jan 2005
Transdniestr

50310 Posts

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)

 2008-12-05, 04:01 #5 CRGreathouse     Aug 2006 597910 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
 2008-12-05, 05:46 #6 grandpascorpion     Jan 2005 Transdniestr 503 Posts Ah, right again. Back to the drawing board ...
2008-12-05, 13:11   #7
CRGreathouse

Aug 2006

3×1,993 Posts

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!)

 2008-12-05, 15:32 #8 grandpascorpion     Jan 2005 Transdniestr 503 Posts 13-bad : 1746334757 14-bad : 3170297129 (minimal primes this time)
2008-12-06, 00:12   #9
CRGreathouse

Aug 2006

3×1,993 Posts

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.

Last fiddled with by CRGreathouse on 2008-12-06 at 00:13

 2008-12-06, 06:05 #10 grandpascorpion     Jan 2005 Transdniestr 7678 Posts By the way, I checked through 4 billion. No results for 15. I'm done for now anyways :)
2008-12-06, 15:38   #11
CRGreathouse

Aug 2006

175B16 Posts

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.

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