Just more "statistical bias in the distribution of primes" or why I should apologize to Google

No, I will never apologize to Google, now called Alphabet - a name easy to remember as most kids' nightmare.

It's basically another evil corporation that, to add insult to injury, actually used to insist on not being evil. Yes, their motto for a long time was "Don't Be Evil" (just google it). They changed it to "Do the right thing" in 2015 in yet another brazen attempt to insult our intelligence.

On the other hand, I am beginning to feel a bit sorry for killing Google so badly. Just look at the screenshot below taken on June 29th in Los Angeles (the time and location may matter for your search results) that shows the first page of Google search results if your keyword happens to be "statistical bias in the distribution of primes".

The five top pages on that first page point in one way or another to my paper "Statistical Bias in the Distribution of Prime Pairs and Isolated Primes" about a significant new effect in the distribution of this fundamental class of integers. Holy moly, Batman!

Well, stuff happens. I doubt this will last forever, or even for a whole month.

Things do change. Or, as one Googler said, "panta rhei." No, he really wasn't a Googler, I just made it up just as Google does it in their mottos, but he sure must have anticipated Google's technology.

P.S.
(1) A few hours later, I actually see 6 top pages on the first page of Google related to this paper or the effect it discusses, one of them belonging to this blog, so I was indeed right more than I could have imagined: things are indeed very fluid in the Google search engine, or "pantarheish," if you will. Even Wikipedia can't compete with me!
(2) Oh, boy. Looks like I have broken Google... It's almost midnight here 29/30 of June and now I am seeing 7 top pages referring to this effect and I swear I am not drinking or smoking anything. In fact, I even took another screenshot to show that I am so totally not making it up. See for yourself below.

"Statistical bias in the distribution of primes" vs "bias in the distribution of primes" in Google

Check out the image below taken on June 21st. You can click on it to enlarge it.

It shows the top of the first page of Google search results for "statistical bias in the distribution of primes" and (hooray!) the first three top pages listed are either to the viXra location of my paper on a statistical bias in the distribution of primes (both twins and isolated prime numbers) or to its two PDF versions: the last one as of this writing (and sixth in general) and the third one.

However, when you search for "bias in the distribution of primes" you will not find any results related to this paper among the 129 pages that Google lists for this keyword.

This seems ridiculous considering how small a difference there is between these two keywords, but unfortunately Google is far from perfect and this sort of instability problem is rather common. Google should probably hire more physicists who understand issues of (in)stability than coding monkeys who apparently don't understand (or care about) that at all.

Incidentally, on June 22nd, "statistical bias in the distribution of primes" has almost gone the way of the other keyword (you can now find only some indirect references to my paper in the lower part of the 2nd page of search results for this keyword), attesting to how volatile Google rankings can really be. It's more than ridiculous. It's just makes no sense at all.

See also my previous post, very much related.

Google on "statistical bias in the distribution of prime numbers"

Curiously enough, as attested by the image below taken on June 20th (click on it to enlarge it), when you search Google for "statistical bias in the distribution of prime numbers," the top two pages displayed are two different PDF versions of my paper on a recently discovered bias in the distribution of primes.

Keep in mind that how Google displays its search results may depend on your location, so you may not see exactly the same thing, although you should (probably) still see these two pages on the first page of Google results. At least, in June 2018, as the positions of sites in Google searchers change with time too.

I am glad to see these pages to rank that high on Google, at least for this keyword that is rather natural. Since the effect discussed in my paper was overlooked for so long and promoting it via more scholarly channels is not always easy (it may take some time to get this this paper posted to sites that attract greater attention of professional mathematicians), it's good to see that Google can be helpful in spreading the word about this effect.

New statistical bias in the distribution of prime numbers

A new pattern in the distribution of primes was uncovered in early February 2018. Apparently, it was overlooked by whole generations of mathematicians despite being rather large. It is a statistical bias, a deviation from what should be expected, in the distribution of prime numbers, that has a slightly different quantitative properties for prime pairs (twins) and isolated primes.

I write about it in two posts on my other (business) blog. The first of stories tells a bit about the bias discovery. The other, more recent, revisits this topic.

The paper that describes this effect in considerable mathematical detail, entitled "Statistical Bias in the Distribution of Prime Pairs and Isolated Primes," can be read online at this preprint repository.