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."

An anonymous reader writes with a report that: Tamar Barbi, a 10th grade student living in Hod Hasharon, Israel, discovered that the theorem she was using to solve one of the problems on her geometry homework didn't actually exist. With the help of her teacher and mathematicians, she wrote up a proof for the theorem, which helps provide new and more elegant proofs for many other mathematical theorems. Posters at Hacker News have some skeptical words about the theorem's novelty, but also about the phrasing of the news report, which seems to omit some crucial words.

An anonymous reader points us to a fascinating piece at The Economist that tries to explain the elements that drive people to work so hard: Working effectively at a good job builds up our identity and esteem in the eyes of others. We cheer each other on, we share in (and quietly regret) the successes of our friends, we lose touch with people beyond our network. Spending our leisure time with other professional strivers buttresses the notion that hard work is part of the good life and that the sacrifices it entails are those that a decent person makes. This is what a class with a strong sense of identity does: it effortlessly recasts the group's distinguishing vices as virtues. This reminds me of an article by Om Malik, veteran reporter and founder of the GigaOm news outlet, who wrote this when announcing his retirement. From his piece: "I relate to Jeter's desire to find life outside of work. Living a 24-hour news life has come at a personal cost. I still wake in middle of the night to check the stream to see if something is breaking, worrying whether I missed some news. It is a unique type of addiction that only a few can understand, and it is time for me to opt out of this non-stop news life."

JoeyRox writes: President Obama said Friday that smartphones -- like the iPhone the FBI is trying to force Apple to help it hack -- can't be allowed to be "black boxes," inaccessible to the government. He believes technology companies should work with the government on encryption rather than leaving the issue for Congress to decide. He went on to say, "If your argument is strong encryption no matter what, and we can and should create black boxes, that I think does not strike the kind of balance we have lived with for 200, 300 years, and it's fetishizing our phones above every other value." Obama's appearance on Friday at the event known as SXSW, the first by a sitting president, comes as the FBI tries to force Apple to help investigators access an iPhone used by one of the assailants in December's deadly San Bernardino, California, terror attack. "The question we now have to ask is, if technologically it is possible to make an impenetrable device or system, where the encryption is so strong there's no key, there's no door at all, then how do we apprehend the child pornographer? How do we solve or disrupt a terrorist plot?" Obama said. "If in fact you can't crack that at all, government can't get in, then everybody's walking around with a Swiss bank account in their pocket." He said compromise is possible and the technology industry must help design it.

HughPickens.com writes: Dana Goldstein writes at Slate that political scientist Andrew Hacker proposes replacing algebra II and calculus in the high school and college with a practical course in statistics for citizenship. According to Hacker, only mathematicians and some engineers actually use advanced math in their day-to-day work and even the doctors, accountants, and coders of the future shouldn't have to master abstract math that they'll never need. For many math is often an impenetrable barrier to academic success. Algebra II, which includes polynomials and logarithms, and is required by the new Common Core curriculum standards used by 47 states and territories, drives dropouts at both the high school and college levels. Hacker's central argument is that advanced mathematics requirements, like algebra, trigonometry and calculus, are "a harsh and senseless hurdle" keeping far too many Americans from completing their educations and leading productive lives. "We are really destroying a tremendous amount of talent—people who could be talented in sports writing or being an emergency medical technician, but can't even get a community college degree," says Hacker. "I regard this math requirement as highly irrational." According to Hacker many of those who struggled through a traditional math regimen feel that doing so annealed their character while critics says that mathematics is used as a hoop, a badge, a totem to impress outsiders and elevate a profession's status. "It's not hard to understand why Caltech and M.I.T. want everyone to be proficient in mathematics. But it's not easy to see why potential poets and philosophers face a lofty mathematics bar. Demanding algebra across the board actually skews a student body, not necessarily for the better."

An anonymous reader writes: Aberrant treatment of transactions by Bitcoin miners has renewed concerns that Bitcoin as a protocol may need a stronger specification. OpenBSD savior and Bitcoin entrepreneur Mircea Popescu raised this issue back in 2013 that the current attitude of "the code is the spec" was introducing fragility and harming Bitcoin's vital decentralization. While a lot of fuss has been made about the maximum blocksize, perhaps formalizing the protocol and breaking the current mining cartel is a more urgent and serious problem. The debate going on resurrects many of Datskovskiy's early concerns about Bitcoin's fragility including mining as a necessary bug, but a bug nonetheless.

Last week you asked questions of Ubuntu Unleashed author Matthew Helmke, about everything from system D to the future of Ubuntu and Canonical; he's responded, at length. Read on for Matthew's answers.

An anonymous reader writes: A recent paper from the University of Illinois at Urbana-Champaign shows that bitcoin mining profits can be increased considerably if mining hardware is allowed to produce occasional errors. The research shows that mining hardware that allows occasional errors ("approximate mining") can run much faster and take up less area than a conventional miner. Furthermore, the errors that are produced by the miner do no corrupt the blockchain since such errors are easily detected and discarded by the bitcoin network. Mining profits can increase by over 30%.

Flash Modin writes: In 1936, twenty years after Albert Einstein introduced the concept, the great physicist took another look at his math and came to a surprising conclusion. 'Together with a young collaborator, I arrived at the interesting result that gravitational waves do not exist, though they had been assumed a certainty to the first approximation,' he wrote in a letter to friend Max Born. Interestingly, his research denouncing gravitational waves was rejected by Physical Review Letters, the journal that just published proof of their existence. The story shows that even when Einstein's wrong, it's because he was already right the first time.

Andy Nicholls has been an R programmer and consultant for Mango Solutions since 2011 (where he currently manages the R consultancy team), after a long stint as a statistician in the pharmaceutical industry. He has a serious background in mathematics, too, with a Masters in math and another in Statistics with Applications in Medicine. Andy has taught more than 50 on-site R training courses and has been involved in the development of more than 30 R packages; he's also a regular contributor to events at LondonR, the largest R user group in the UK. But since not everyone can get to London for a user group meeting, you can get some of the insights he's gained as an R expert in Sams Teach Yourself R In 24 Hours (available in print or at Safari), of which he is the lead author. Today, though, you can ask Andy about the much-lauded statistics-oriented free software (GPL) language directly -- Why to use it, how to get started, how to get things done, and where those intriguing release names come from. (The about page is helpful, too.) As usual, please ask as many questions as you'd like, but one question at a time, please.

AthanasiusKircher writes: The Atlantic has an >extended article on the recent surge in advanced math education at the primary and secondary levels in the U.S., arguing that last year's victory for the U.S. in the Math Olympiad was not a random anomaly. Participation in math camps, after-school or weekend math "academies," and math competitions has surged in recent years, with many programs having long wait lists. Inessa Rifkin, co-founder of one of these math academies, argues that the problems with math education begin in the 2nd and 3rd grades: ""The youngest ones, very naturally, their minds see math differently.... It is common that they can ask simple questions and then, in the next minute, a very complicated one. But if the teacher doesn't know enough mathematics, she will answer the simple question and shut down the other, more difficult one." These alternative math programs put a greater focus on problem-solving: "Unlike most math classes, where teachers struggle to impart knowledge to students—who must passively absorb it and then regurgitate it on a test—problem-solving classes demand that the pupils execute the cognitive bench press: investigating, conjecturing, predicting, analyzing, and finally verifying their own mathematical strategy. The point is not to accurately execute algorithms, although there is, of course, a right answer... Truly thinking the problem through—creatively applying what you know about math and puzzling out possible solutions—is more important."

The article concludes by noting that programs like No Child Left Behind have focused on minimal standards, rather than enrichment activities for advanced students. The result is a disparity in economic backgrounds for students in pricey math activities; many middle-class Americans investigate summer camps or sports programs for younger kids, but they don't realize how important a math program could be for a curious child. As Daniel Zaharopol, founder of a related non-profit initiative, noted in his searches to recruit low-income students: "Actually doing math should bring them joy."

An anonymous reader writes: The BBC has now put the second of Stephen Hawking's Reith Lectures up on their web site, with accompanying illustrations. It's not 'All you ever wanted to know about Black Holes', but it's an easy introduction to some of the latest thinking on them.

theodp writes: Teaching kids computer science is a great movement," writes HS senior David Yue, "however, to overly dilute the magnitude of the difficulty in regards to the subject area of coding and to create the illusion of mastering a 'superpower' (Code.org) is a huge mistake. There are many videos and articles on the Internet these days that have demonstrated positive support towards computer science education. Below these articles, one can find many comments, left mostly by parents and supporters. These people usually express how proud they are that their children have an opportunity to learn computer science or how proud they are that computer science is being integrated at a more substantial level into the education system." But Drag and Drop Doesn't = Coding, argues Yue. "Parents and teachers today who aren't technical need to be aware that the drag and drop code or the candy-coated learning process does not effectively teach children programming but eventually causes a huge amount of shock once they are immersed in real code." Yue's Emperor's-New-Code warning comes days before President Obama — a graduate of Code.org's drag-and-drop Disney Princess coding tutorial — asks Congress for $4-billion-and-change in the upcoming budget to fund his "Computer Science for All" K-12 initiative.

An anonymous reader writes: Bitcoin capitalist Mircea Popescu has opened a contest to find a new block cipher and is offering a 10 Bitcoin reward for a winning submission. The eccentric Popescu was previously featured on Slashdot for saving OpenBSD from their electric bill in their time of need.

schwit1 writes: While it was hard to call a winner between Hillary Clinton and Bernie Sanders last night, it's easy to say who was luckier. The race between the Democrat presidential hopefuls was so tight in the Iowa caucus Monday that in at least six precincts, the decision on awarding a county delegate came down to a coin toss. And Clinton won all six, media reports said.

sciencehabit writes: Tracking and recording the motion of the sun, the moon, and the planets as they paraded across the desert sky, ancient Babylonian astronomers used simple arithmetic to predict the positions of celestial bodies. Now, new evidence reveals that these astronomers, working several centuries B.C.E., also employed sophisticated geometric methods that foreshadow the development of calculus. Historians had thought such techniques did not emerge until more than 1400 years later, in 14th century Europe.

An anonymous reader writes: Who doesn't love a good conspiracy theory? Well, I don't — they're usually annoying daydreams from annoying people. Fortunately, an Oxford mathematician seems to feel the same way. Dr. David Grimes just published research in PLOS One establishing a formula for determining the likelihood of a failed conspiracy — in other words, how likely some of its participants are to spill the beans. There are three main factors: number of conspirators, the amount of time passed since it started, and how often we can expect conspiracies to intrinsically fail (a value he derived by studying actual conspiracies that were exposed). From the article: "He then applied his equation to four famous conspiracy theories: The belief that the Moon landing was faked, the belief that climate change is a fraud, the belief that vaccines cause autism, and the belief that pharmaceutical companies have suppressed a cure for cancer. Dr. Grimes's analysis suggests that if these four conspiracies were real, most are very likely to have been revealed as such by now. Specifically, the Moon landing 'hoax' would have been revealed in 3.7 years, the climate change 'fraud' in 3.7 to 26.8 years, the vaccine-autism 'conspiracy' in 3.2 to 34.8 years, and the cancer 'conspiracy' in 3.2 years."

peetm writes: I have an above averagely bright nephew, aged 10, who's into maths and whose birthday is coming up soon. I'd like to get him a suitable present – most likely one that's mathematically centred. At Christmas we sat together while I helped him build a few very simple Python programs that 'animated' some simple but interesting maths, e.g., we built a factorial function, investigated the Collatz conjecture (3n + 1 problem) and talked about, but didn't implement Eratosthenes' Sieve – one step too far for him at the moment perhaps. I've looked about for books that might blend computing + maths, but haven't really found anything appropriate for a 10-year-old. I should be indebted to anyone who might suggest either a suitable maths book, or one that brings in some facet of computing. Or, if not a book, then some other present that might pique his interest.

theodp writes: GeekWire reports that Melinda Gates concluded a Davos panel discussion about gender parity with a personal story about her own family, explaining how she originally became interested in computer science, and how she later played Lab Manager to Bill's Mr. Wizard to help pass along their passion for science and math to their kids. "On Saturday mornings," Gates explained, "I wanted to sleep late. So you know what I did? I made sure there were science projects available, and that's what he did with our two daughters and our son. And guess what my two daughters are interested in? Science and math."

mspohr writes: This article makes a fairly persuasive argument for the utility of the blockchain. It discusses a wide variety of companies and government exploring blockchain to maintain secure records which cannot be altered. One interesting application is to use blockchain to maintain property records in many countries where these records are often incomplete and are easily corrupted (intentionally or unintentionally). A linked article in The Economist expands the thought and discusses changes to the blockchain to improve performance, reduce overhead and accommodate different uses. (See also this related poll.)