Prime numbers: You’ll want to factor this in

[Quartz Obsession] Prime numbers February 07, 2018 Luck of the draw --------------------------------------------------------------- In late December, an electrical engineer in Tennessee using a church computer [discovered]( the largest known prime number ever. Jonathan Pace is one of the volunteers participating in the Great Internet Mersenne Prime Search. That’s right: [GIMPS](. A prime number is a number that’s only divisible by 1 and itself. It’s relatively simple to spot low primes such as 7, 17, or 53, but larger primes are much more difficult to identify. And Mersenne primes, named after a 17th-century French monk, [are a special breed:]( They’re prime numbers that are one less than a power of two—making them even more rare. Since 1996, GIMPS volunteers have discovered 16 new numbers. “There are tens of thousands of computers involved in the search,” Pace told the [New York Times](. “On average, they are finding less than one a year.” Pace had been hunting for one for more than 14 years. The prime he discovered (notated as 2^77,232,917-1) contains 23,249,425 digits—nearly a million digits longer than the previous record holder. That’s exciting in its own right (c’mon, it is!) but the search for large prime numbers is more than just a mathematical treasure hunt. Cryptologists can use these large primes to encrypt security keys—plus the search for large primes [could help improve]( the process of [mining for bitcoin](. 🌐 [View this email on the web]( By the digits [50:]( Number of Mersenne primes that have been discovered. [4:]( Number of computers and hardware configurations used to independently verify the new prime. [$3,000:]( Amount the finding is eligible for (in the form of a GIMPS research award). [$100,000:]( Prize winnings for the first Mersenne prime with at least 10 million digits, discovered in 2008 by using a UCLA computer. Watch this! Primetime security --------------------------------------------------------------- A quick primer (sorry!) on how primes keep your information secure. Persons of interest The heroes of uselessness --------------------------------------------------------------- For centuries, the nagging question that math teachers love to loathe—When am I ever going to use this?—plagued the search for prime numbers. Mathematicians believed that primes were a novelty with no practical application. And some of them preferred it that way. Take G. H. Hardy: One of the most brilliant mathematicians of the 20th century, Hardy avoided “practical” mathematics, believing that “useful” math was dull and too often exploited for military gain. In fact, he wrote an [apologia]( defending math for math’s sake. “I have never done anything ‘useful,’” he wrote. “No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.” Hardy was too smart for his own good. His discoveries were useful: They’ve aided the fields of genetics research, quantum physics, and thermodynamics. Today, his research on the distribution of prime numbers is the bedrock for our [current understanding]( of how prime numbers operate. Oddly satisfying There’s an algorithm for that! --------------------------------------------------------------- The ancient Greeks came up with a system [called the Sieve of Eratosthenes]( for easily determining which numbers are prime. It works by simply eliminating the multiples of each prime number. Any numbers left over will be prime. (The ancient Greeks couldn’t do this in gifs, though.) 🐦 [Tweet this card]( Handy guide Three uses for prime numbers --------------------------------------------------------------- 1) Getting into Gear Before primes were used to encrypt information, their only true practical use was at the auto-body shop. The gears in a car—and every other machine—work most reliably when the teeth are arranged by prime numbers. When gears have 13 or 17 or 23 teeth, it ensures that every gear combination is used, which helps to evenly distribute dirt, oil, and overall wear and tear. 2) Talking with Aliens In his sci-fi novel [Contact, Carl Sagan]( suggested that humans could communicate with aliens through prime numbers. This wasn’t a new idea. In the summer of 1960, the National Radio Astronomy Observatory searched for intelligent extraterrestrial messages by searching for prime numbers. Years later, the astronomer Frank Drake [proposed]( that humans could communicate with aliens by transmitting “semiprimes”—that is, multiples of two prime numbers—into space. 3) Making Nature’s Music The French modernist composer Olivier Messiaen wrote music containing transcribed birdsong and prime numbers, which helped create unusual and unpredictable rhythms, note durations, and time signatures. Messiaen, a Roman Catholic, said that musical prime numbers represented the indivisibility of God. His Liturgie de Cristal is a grand example. Listen to Messien put [prime numbers into practice here](. quotable “Primes seem to me to be these unarbitrary, unique, fated things. It cannot be coincidence that the mythical numbers of storytelling like 3, 7, and 13 are random. The lower-end primes have incredible resonance in fiction and art.” — Robin Sloan, who wrote the bestselling mystery [Mr. Penumbra’s 24-Hour Bookstore,]( in which [every number was a prime (except 24 of course)](. What’s the buzz? Cicadas: Nature’s number-crunchers --------------------------------------------------------------- Animal populations rise and fall in cycles. When resources are plentiful, a local population of herbivores may boom—which helps increase the population of predators. Eventually, this surge of life stresses the environment, resources are gobbled up, and the population drops. This gives plant life a chance to recover, which ultimately leads to another boom, which leads to another drop, and so on… These cycles are consistent and predictable. In fact, they’re so predictable that cicadas of the genus magicicada have evolved to avoid them by exploiting the power of prime numbers—the broods only emerge at intervals of 13 or 17 years. Patrick de Justo at [The New Yorker]( explains how this works: “Cicadas that emerge at prime-numbered year intervals, like the seventeen-year Brood II set to swarm the East Coast, would find themselves relatively immune to predator population cycles, since it is mathematically unlikely for a short-cycled predator to exist on the same cycle … [A] cicada that emerges every seventeen years and has a predator with a five-year life cycle will only face a peak predator population once every eighty-five (5 x 17) years, giving it an enormous advantage over less well-adapted cicadas.” In 2004, Researchers at Brazil’s Universidade Estadual de Campinas confirmed this theory, concluding that a “[prime-numbered life cycle had the most successful survival strategy]( Pop Quiz The number 10^30 + 666 × 10^14 + 1 is called what? Satan’s PalindromeThe Devil’s DigitBelphegor’s PrimeBeelzebub’s Address Correct. 1000000000000066600000000000001: This “palindromic prime” contains a one, 13 zeroes, a 666, 13 more zeroes, followed by another one, and is named for one of the seven demon princes of Hell. Incorrect. If your inbox doesn’t support this quiz, find the solution at bottom of email. Fun fact! An emirp (get it?) is a prime number that, when its decimal digits are reversed, results in a different prime. Think 13, 17, 31, 37, 71, 73, 79 …. According to Wikipedia, the largest known emirp is [10^10006+941992101×10^4999+1.]( The loneliest number Is one prime? --------------------------------------------------------------- Mathematicians have been debating this question for centuries. In fact, the answer is still [being pondered](. Here’s a look at what different great minds believed. [Screen Shot 2018-02-07 at 2.04.40 PM] Poll What do you think of prime numbers now? [Click here to vote]( Depressing that cicadas are better at math than I am.Still waiting to hear back from my alien pen pal.Where shall I put my 1000000000000066600000000000001 tattoo? The fine print In yesterday’s poll about the [Voynich manuscript]( 41% of you said you’re “ready for a new internet mystery.” Today’s email was written by [Lucas Reilly](. 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