[seqfan] Re: A075323

Hans Havermann gladhobo at teksavvy.com
Thu Nov 27 14:40:15 CET 2014


Good catch! My sense is that (659, 2671), like the earlier (89, 599), is a small-numbers fluke that will not be repeated. Doesn't asking for a partner (say x) to either 2683 or 2687 require that x *not* be partnered with a larger number, which in turn requires very large prime gaps to appear way before they ever actually do appear? Don, you should add the two numbers as likely exceptions to the question.

http://chesswanks.com/num/a075323.png

> On Nov 26, 2014, Don Reble wrote:
> 
>> %C A075323 Question: Is every [odd] prime a member of some pair?
> 
>   Perhaps not. In the first 40982 pairs, every odd prime below 1000000
>   appears, except for 2683 and 2687. Maybe they never appear.
>   On the other hand, there are some surprises, such as pair #1006.
> 
>   1003 16421 18427
>   1004 16453 18461
>   1005 16573 18583
>   1006   659  2671
>   1007 16603 18617
>   1008 16381 18397
>   1009 16619 18637


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