Primorial Sequence Question

grandpascorpion · 2006-02-23, 21:40

Hello folks,

Sorry in advance for referring back to the Prime Puzzles website (specifically this week's puzzle: http://www.primepuzzles.net/puzzles/puzz_350.htm)

In short, the puzzle is:

For each q=>2, find the smallest prime p such that p>q# & (p-r#) is prime for all prime r<=q.

Actually, I wrote something in PARI for this and have extended the table through p=37 but I was wondering if anyone had heard of prior work on this sequence. I did a cursory check of the Integer Sequences site but couldn't find this one.

To be honest, I'd be a little surprised if no one has worked on this curio before. The numbers are involved are tiny, relatively speaking.

Thanks,
Grandpa

Citrix · 2006-02-24, 01:59

GS, if you find a case for q=101, don't you eliminate all numbers below it?

grandpascorpion · 2006-02-24, 15:01

The puzzles asks for the smallest prime for each prime q.

The answer for q=101 would almost certainly be larger then q=97 or less.

2006-02-23, 21:40	#1
grandpascorpion Jan 2005 Transdniestr 503 Posts	Primorial Sequence Question Hello folks, Sorry in advance for referring back to the Prime Puzzles website (specifically this week's puzzle: http://www.primepuzzles.net/puzzles/puzz_350.htm) In short, the puzzle is: *For each q=>2, find the smallest prime p such that p>q# & (p-r#) is prime for all prime r<=q.* Actually, I wrote something in PARI for this and have extended the table through p=37 but I was wondering if anyone had heard of prior work on this sequence. I did a cursory check of the Integer Sequences site but couldn't find this one. To be honest, I'd be a little surprised if no one has worked on this curio before. The numbers are involved are tiny, relatively speaking. Thanks, Grandpa Last fiddled with by grandpascorpion on 2006-02-23 at 21:43

2006-02-24, 15:01	#3
grandpascorpion Jan 2005 Transdniestr 503 Posts	Smallest prime The puzzles asks for the smallest prime for each prime q. The answer for q=101 would almost certainly be larger then q=97 or less.

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2006-02-24, 01:59	#2
Citrix Jun 2003 62B₁₆ Posts	GS, if you find a case for q=101, don't you eliminate all numbers below it?