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Old 2008-12-03, 20:26   #1
davar55
 
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Default 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)?
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Old 2008-12-04, 19:46   #2
grandpascorpion
 
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Isn't 2 the first 1-bad number?
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Old 2008-12-04, 19:49   #3
CRGreathouse
 
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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
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Old 2008-12-04, 22:28   #4
grandpascorpion
 
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Quote:
Originally Posted by CRGreathouse View Post
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)
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Old 2008-12-05, 04:01   #5
CRGreathouse
 
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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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Old 2008-12-05, 05:46   #6
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Ah, right again. Back to the drawing board ...
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Old 2008-12-05, 13:11   #7
CRGreathouse
 
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13 1746334757

Quote:
Originally Posted by grandpascorpion View Post
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!)
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Old 2008-12-05, 15:32   #8
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13-bad : 1746334757
14-bad : 3170297129

(minimal primes this time)
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Old 2008-12-06, 00:12   #9
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Quote:
Originally Posted by grandpascorpion View Post
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
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Old 2008-12-06, 06:05   #10
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By the way, I checked through 4 billion. No results for 15. I'm done for now anyways :)
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Old 2008-12-06, 15:38   #11
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Quote:
Originally Posted by grandpascorpion View Post
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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