I don't have much time to work on this issue right now, and this will not change a lot until perhaps later this year, but I did make some additional empirical studies over this past weekend and it looks that my paper on this statistical effect in the distribution of primes might have only scratched the surface of what seems to be a more complex phenomenon.
In particular, this effect appears to have somewhat similar qualities to another effect in the distribution of primes that was discovered in the late 90s. I have discovered 3 new instances of this effect, if one is willing to generalize it a bit, over the last few days.
I think this effect deserves its own name and perhaps its own paper that introduces it properly. Let's call this a work in progress.
I will continue investigating it as much as my time permits, and then will probably issue yet another version of my paper. I am beginning to wish I waited with its publication as this is now consuming more of my time and thinking than I can afford at this point. But then again, I might have never published it had I not done it in April.
Monday, July 9, 2018
Saturday, July 7, 2018
The popularity of my paper on the bias in the distribution of primes keeps on growing
The interest in this paper continues to grow.
At least, as measured by the number of its downloads from the viXra site, which hosts the paper in question, "Statistical Bias in the Distribution of Prime Pairs and Isolated Primes." The number of the downloads has now reached 30.
The paper was originally posted there on 4/27/2018. Note that 4/27 is 2^2/3^3, but I did not really chose to post it on a special day like that. Still, it's easier to remember this date that way.
At least, as measured by the number of its downloads from the viXra site, which hosts the paper in question, "Statistical Bias in the Distribution of Prime Pairs and Isolated Primes." The number of the downloads has now reached 30.
The paper was originally posted there on 4/27/2018. Note that 4/27 is 2^2/3^3, but I did not really chose to post it on a special day like that. Still, it's easier to remember this date that way.
It is probably safe to predict that the number of downloads of this paper will reach 50 by the end of 2018.
With 30 downloads so far, it's already the most popular of my papers posted on viXra.org this year despite being the newest of them. It stands a chance to become the most popular of all my papers there given some time; say, by the end of 2020.
To be honest, my other papers there are of little consequence in a grander scheme of things, that's why they all are entitled "A note on ... ." Just mere notes on what can probably be fittingly described as mathematical curiosities of one kind or another. Nothing wrong with that per se, but they add very little to mathematics, and have never meant to be published anywhere else.
The paper on the bias in the distribution of primes is different, though, as being about rather large and overlooked an effect in the distribution of a very important class of natural numbers.
The most popular papers on viXra (at least when it to comes to number theory, which interests me most) are not necessarily groundbreaking, but, as you can easily verify for yourself, those dealing with the Riemann Hypothesis, simpler proofs of the Fermat Last Theorem, proofs of the Collatz Conjecture, anything to do with Pi or Golden Ratio, etc. In other words, papers dealing with popular, attractive topics rather than concerned with novel phenomena as is the case for my paper.
Needless to say, because of this bias towards hard to prove conjectures that can really be only appreciated by professionals with many years of study and a good background in mathematics, viXra has a reputation for attracting crackpots, but that does not mean that everything that gets posted there should be dismissed by default. I like to judge things on their individual merits. I may not be in the majority in this regard, but that suits me just fine as I tend to be a contrarian by nature.
Besides attracting crackpots, viXra stands out in yet another way: it draws the hate of elitists and people quick to judge by appearances often referred to as bigots. I suspect that there is a large overlap between these two groups. Since such people elicit in me a full spectrum of only negative reactions, the fact they hate it, makes me even more supportive of it. Overall, I think that "viXra is a good thing" - thanks Martha Stewart!
Incidentally, I recently managed to submit my paper to arXiv, a much more popular e-print repository than viXra and seen as more respectable. That took some time. Despite starting my submission efforts about the time I posted the first version of the paper to viXra, I fully succeeded only in early July. The requirement of securing at least one endorsement from a professional researcher with a right to serve as an arXiv endorser can be a bit of an annoying obstacle, but once you overcome it, you feel vindicated in the value of your paper.
The most popular papers on viXra (at least when it to comes to number theory, which interests me most) are not necessarily groundbreaking, but, as you can easily verify for yourself, those dealing with the Riemann Hypothesis, simpler proofs of the Fermat Last Theorem, proofs of the Collatz Conjecture, anything to do with Pi or Golden Ratio, etc. In other words, papers dealing with popular, attractive topics rather than concerned with novel phenomena as is the case for my paper.
Needless to say, because of this bias towards hard to prove conjectures that can really be only appreciated by professionals with many years of study and a good background in mathematics, viXra has a reputation for attracting crackpots, but that does not mean that everything that gets posted there should be dismissed by default. I like to judge things on their individual merits. I may not be in the majority in this regard, but that suits me just fine as I tend to be a contrarian by nature.
Besides attracting crackpots, viXra stands out in yet another way: it draws the hate of elitists and people quick to judge by appearances often referred to as bigots. I suspect that there is a large overlap between these two groups. Since such people elicit in me a full spectrum of only negative reactions, the fact they hate it, makes me even more supportive of it. Overall, I think that "viXra is a good thing" - thanks Martha Stewart!
Incidentally, I recently managed to submit my paper to arXiv, a much more popular e-print repository than viXra and seen as more respectable. That took some time. Despite starting my submission efforts about the time I posted the first version of the paper to viXra, I fully succeeded only in early July. The requirement of securing at least one endorsement from a professional researcher with a right to serve as an arXiv endorser can be a bit of an annoying obstacle, but once you overcome it, you feel vindicated in the value of your paper.
Wednesday, July 4, 2018
"Prime distribution bias" according to Google
This Google thing can be pretty fun.
Especially, when it puts links to your stuff in the top of page one of its search results. Otherwise less so, although anything that lands on the first page of Google's search results is good too. The second page is still acceptable. The third one? I have mixed feelings about that.
Let's see what this Google thing has produced for the keyword proudly displayed in the title of this article. Well, it turns out that the very top link on the first page of results for this glorious keyword is to my paper on arXiv about a recently discovered bias in the prime distribution. I submitted this paper there just a few days ago as also mentioned in my previous post here.
See another screenshot taken on July 4th documenting this event.
As long as this top link stays there, I promise to forget how "evil" Google can be.
Especially, when it puts links to your stuff in the top of page one of its search results. Otherwise less so, although anything that lands on the first page of Google's search results is good too. The second page is still acceptable. The third one? I have mixed feelings about that.
Let's see what this Google thing has produced for the keyword proudly displayed in the title of this article. Well, it turns out that the very top link on the first page of results for this glorious keyword is to my paper on arXiv about a recently discovered bias in the prime distribution. I submitted this paper there just a few days ago as also mentioned in my previous post here.
See another screenshot taken on July 4th documenting this event.
As long as this top link stays there, I promise to forget how "evil" Google can be.
Tuesday, July 3, 2018
My paper on the prime number bias is now on arXiv
I was able to find a professional number theorist who agreed to endorse my paper on this effect (statistical bias) in the distribution of primes for arXiv. I am pleased to say that not only is he a well-regarded mathematician, but probably also best qualified to judge the value of my paper as an expert in probabilistic number theory.
It is not so easy to submit your paper there if you are not affiliated with any academic institution as is my case theses days. Though I did post 11 papers on arXiv in the 90s, and most if not all have citations of other researchers, they are in the physics part of this well-known e-print repository. This one is my first serious attempt at experimental number theory, so I wanted to get it posted in math.NT as this is the most suitable section for this type of papers.
The paper has the same title as its earlier versions, Statistical Bias in the Distribution of Prime Pairs and Isolated Primes.
As I say in the last section of the paper, more empirical work is still needed to understand this bias, which is not a minuscule phenomenon by any reasonable standards. On the contrary, it is pretty substantial. It is easy to grasp too, which should make it of interest to the public at large and not only to number theorists. Also, and even more importantly, we need a theoretical model to explain it. At this point, I have neither time nor resources to study it beyond what I have done already, but I hope others do.
It is not so easy to submit your paper there if you are not affiliated with any academic institution as is my case theses days. Though I did post 11 papers on arXiv in the 90s, and most if not all have citations of other researchers, they are in the physics part of this well-known e-print repository. This one is my first serious attempt at experimental number theory, so I wanted to get it posted in math.NT as this is the most suitable section for this type of papers.
The paper has the same title as its earlier versions, Statistical Bias in the Distribution of Prime Pairs and Isolated Primes.
As I say in the last section of the paper, more empirical work is still needed to understand this bias, which is not a minuscule phenomenon by any reasonable standards. On the contrary, it is pretty substantial. It is easy to grasp too, which should make it of interest to the public at large and not only to number theorists. Also, and even more importantly, we need a theoretical model to explain it. At this point, I have neither time nor resources to study it beyond what I have done already, but I hope others do.
Friday, June 29, 2018
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.
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.
Friday, June 22, 2018
"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.
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.
Thursday, June 21, 2018
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.
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.
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