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Sarah Carlton (Formerly Sarah Pagan)
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That moment when Golbat wants to eat your face...
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So Google+ just asked me why I was using it today. They didn't have an option for "I'm stuck on the internet clicking all my favorite buttons like a rat with a lever, not yet awake/self-aware enough to get offline yet"

I decided "interacting with an online community" was close enough.
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Are you using G+ or is G+ really using you?
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So I'm going through my childhood stuff, and I come across these super cool Harry Potter socks that I forgot existed. Bonus: they were too big for me as a kid, but now they'll fit great!
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You are FREEEE !
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These guys are back! I loved watching this show.
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So I didn't know that an excellent throw was possible. Much less on a curve ball. Much less at a stupid Golbat. (This was my 5-7th throw) I'm pretty proud of this throw!
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Good job!
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This is so cool!
(Japanese article) Watson saves Japanese woman's life by correctly identifying her disease after treatment failed. Her genome was analyzed and the correct diagnosis was returned in ten minutes. Apparently first ever case of a life directly being saved by an AI in Japan. | r/Futurology at reddit.com
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I discovered my Patronus is a Kingfisher on J.K Rowling’s Pottermore. Find out yours now:
+Rita Pagan I knew it'd be a bird :D
Pottermore Patronus
Written by J.K. Rowling, created by Pottermore, discover your Patronus now.
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+Rita Pagan :) You have to create an account on Pottermore to do it. But I think it's worth the effort; it's a very polished and immersive experience. Try it out!
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sigh I guess I'll have to make another sheet.
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Yeah, no choice really. 
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Adulthood = Chocolate cake for breakfast.
Pretty sure.
Yep.
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This is beautiful. I will use Yelp a lot more often now!
 
Now here's a way to find those Pokéstops
If you're already looking for a nice place to grab some dinner for you and the Mrs, why not grab some Pokemon Go supplies while you're at it? Joining the list of companies looking to capitalize on the recent Pokemon Go craze is Yelp who now has a filter in their app for searching restaurants and businesses with nearby PokeStops. Just open the app, tap on the filter button (right next to search), and scroll down to turn on the PokeStop Nearby filt...
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Beautiful math!

h/t +Yonatan Zunger
 
Primes with no sevens

This is a prime number whose decimal digits are all ones.  It has 317 ones.  It's not the world record.  The number with 1031 ones is also known to be prime! 

Even larger guys like this are suspected  to be prime.  Are there infinitely many?   Mathematicians believe so, but they can't prove it.

Why do they believe it?   The main reason is that they have an estimate of the "probability" that a number with some number of digits is prime. We can use this to guess the answer to this puzzle.

Of course the whole idea of "probability" is a bit weird here.  A number is either prime or not: the math gods do not flip coins to decide which numbers are prime! 

Nonetheless, treating primes as if  they were random turns out to be useful.   Mathematicians have made many guesses using this idea, and then proved these guesses are right, using a lot of extra work.

Of course it's subtle.  If I wrote down a number with 317 twos in its decimal expansion, you'd instantly know it's not prime - because it would be even.

In the European Congress of Mathematics, a number theorist named James Maynard just announced something cool.  There are infinitely many prime numbers with no sevens in their decimal expansion!

And his proof works equally well for any other number: there infinitely many primes without 0 as a digit, or 1, or 2, or 3, or 4, or 5, and so on.

This is big news, but not because mathematicians really care about primes with no sevens in them.  It's because proving something like this requires a deep and delicate understanding of "the music of primes" - the way prime numbers are connected to wave patterns.  For more on that, here's something easy to read:

https://plus.maths.org/content/missing-7s

Thanks to +Luis Guzman for pointing out this article, and thanks to +David Roberts for finding James Maynard's paper on this subject, which is here:

• James Maynard, Primes with restricted digits, http://arxiv.org/abs/1604.01041.

He shows that if your base b is sufficiently large, you can find infinitely many primes that are lacking a chosen set of digits, where this set can contain up to b^(23/80) of the digits.  Unfortunately I don't see  how large b must be - he may not have worked this out.  If b = 10 counts as sufficiently large, then since 10^(23/80) is about 1.94, this result would let you avoid any one digit in base 10, but not two.  In any event, he does prove, separately, that you can find infinitely many primes that avoid any one digit in base 10.

  It uses cool techniques, like "decorrelating Diophantine conditions which dictate when the Fourier transform of the primes is large from digital conditions which dictate when the Fourier transform of numbers with restricted digits is large".  It also uses ideas from Markov process theory - that is, the theory of random processes - as well as hard-core number theory concepts.

#bigness   #spnetwork arXiv:1604.01041 #numberTheory #primes  
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I love to laugh!
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I'm just a girl.

Just a girl who's studying Computer Science, loves everything Google, wants make neat things with code, and eventually be an awesome teacher so I can pay it forward.
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Sarah Carlton (Formerly Sarah Pagan)'s +1's are the things they like, agree with, or want to recommend.
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