Friday, October 25, 2019

The Twittersphere…

Some things I’ve touted on Twitter lately:

1)  I listen to several weekly podcasts, but oddly very few math podcasts. Still, am surprised (embarrassed?) I was unaware of the “Breaking Math” podcast that apparently has been around for awhile. Caught my attention because of the current session done with Ben Orlin (he's this cartoony guy who thinks he can write math books that blogger-dupes will fall in love with and recommend non-stop ;), but so many of their past episodes look great as well:

2)  Always fun, the latest online issue of Chalkdust magazine is out now:

3)  I linked earlier (on Twitter) to this short inquiry from Ken Abbott’s blog (quoted verbatim below), related to ever-fascinating prime number pattern/distribution, but never saw any response to it (Ken doesn’t seem to have a “comments” section on his blog and I don’t know if anyone responded to him via email?):

About the distribution of Twin Primes. 
Let p1 be the first prime of a twin prime pair and let p2 be the first prime of the next consecutive twin prime pair. Then, I'm quite surprised how small p2-p1 stays. And when it does increase it will suddenly drop back to a very small number such as 12. 
Anybody have any input on this?

I also asked, but never got a response, if there was some table readily available on the Web of such p2-p1 values? Or, more generally, any papers out there that have studied this particular set of values? (surely someone has?)

==> ADDENDUM:  It occurred to me that the wonderful OEIS site would likely have something on this, and typing in the first several p2-p1 values, sure enough it is there:

a list of values:

(first ~140 values given with a highest value attained of 150, and constantly returning to low value of 6)

and more general info/links:

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