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Mathematicians Discover Prime Conspiracy (quantamagazine.org)
An anonymous reader writes with an intriguing story at Quanta Magazine, which begins: Two mathematicians have uncovered a simple, previously unnoticed property of prime numbers — those numbers that are divisible only by 1 and themselves. Prime numbers, it seems, have decided preferences about the final digits of the primes that immediately follow them. Among the first billion prime numbers, for instance, a prime ending in 9 is almost 65 percent more likely to be followed by a prime ending in 1 than another prime ending in 9. In a paper posted online today, Kannan Soundararajan and Robert Lemke Oliver of Stanford University present both numerical and theoretical evidence that prime numbers repel other would-be primes that end in the same digit, and have varied predilections for being followed by primes ending in the other possible final digits. "We've been studying primes for a long time, and no one spotted this before," said Andrew Granville, a number theorist at the University of Montreal and University College London. "It's crazy."
https://www.quantamagazine.org...
And stop linking to the news article only, without linking to the scientific paper. Just for those who care, here is the link: http://arxiv.org/pdf/1603.0372...
If you rtfa it says "Lemke Oliver and Soundararajan discovered that this sort of bias in the final digits of consecutive primes holds not just in base 3, but also in base 10 and several other bases; they conjecture that it’s true in every base. "
Why would you think that? The laws of division don't change for different base representations. Division is division no matter how you write the number.
Learning HOW to think is more important than learning WHAT to think.
Oh for FFS. The US did not bait Japan with the fleet at Pearl Harbor. That was the home port long before they embargoed Japan and if they had move the fleet to the west coast then Japan would have just attacked the Philippines and you would be talking about how suspicious it was that US moved their fleet away from the Philippines after they embargoed Japan. If you're trying to start a war you don't make your opening move laying your most important assets out for the enemy to wipe out, you stage something that you control. Like Poland "attacking" Germany or having WMD's.
The fleet was lined up in Pearl Harbor because the US military had been stripped down after WWI and was run by politically motivated officers who often didn't know their arse from a hole in the ground (the prima donna General MacArthur being the prime example). Once war broke out those officers were quickly squirreled away and better officers brought up from the ranks who actually knew what they were doing. Most people don't realize that Eisenhower was a Major with no combat experience who was quickly promoted up to General because Marshall knew he had a sharp strategic mind (and could put up with politics, which he demonstrated as a member of MacArthur's staff). The German general staff couldn't (and for a time didn't) believe he was made Allied Supreme commander instead of Patton (who was tactically brilliant but questionable strategically and certifiably insane to boot).
> What's this base 1010 drama? Everyone knows in binary ALL primes end in "1".
In binary ALMOST all primes end in "1".
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WTF? Why, in the name of all that's good, would they...
Oh, I just noticed. You're still new here. *sighs*
Look, nobody reads the article. Nobody is going to read a scientific paper. Well, a few of us might read the article (I'm not admitting to anything) but those of us who do, also know how to find the applicable paper.
If you look at the very top post in the thread, there's someone bitching that there is no link to the article. Yet, the article link is right next to the title - where it has been for almost a year now. (They're sometimes in the summary as well. Not always.) That should tell you, they being a representative of the average one of us, how often we actually even read the article - or even look for the URL.
They're not going to do it. The two other people who read the article know where Arxiv is. The editor would have to, you know, work. Ain't happening. Submit stories with the link included if you're passionate. 'Snot going to change in your lifetime. You're probably the 10,985,729th (see what I did there?) person to suggest that - this month.
"So long and thanks for all the fish."
There are very few numerical properties that are base-dependent.
Some of the little tricks they teach you in school are strictly base-dependent, like if a decimal number ends in 5 or 0 it's divisible by 5 or 10 respectively. If a decimal number ends in a value divisible by 2 it's even else odd. Or if a decimal number's digits sum to a multiple of 3 or 9 then it's divisible by 3 or 9 respectively.
What they don't tell you is that is generalizable to other bases. Generically speaking if the final digit of a number in a given base is divisible by any factor of that base then the number itself is divisible by that factor (this should be fairly obvious) and if the digits of a number sum to a number divisible by a factor of (base-1) then that number itself is divisible by that factor (less obvious, but provable).
So for hex, for example, the factors of 16 are 2, 4, 8, 16. If a number in base-16 ends in 0 it's obviously divisible by 16, if it ends in 8 then it's divisible by 8 and so on. The factors of (16-1)=15 are 3, 5, and 15. So if the sum of digits of a hex number are divisible by 3, 5, or 15 then the number is also divisible by 3, 5, or 15 respectively as well.
Fun little math quirks on bases.