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"Twin primes" are primes that are two steps apart from each other on that line: 3 and 5, 5 and 7, 29 and 31, 137 and 139, and so on. The twin prime conjecture states that there are infinitely many twin primes, and that you'll keep encountering them no matter how far down the number line you go. It also states that there are infinitely many twin primes, and that you'll keep encountering them no matter how far down the number line you go. It also states that there are infinitely many prime pairs with every other possible gap between...

Belphegor's prime number Belphegor's prime number is a palindromic prime number with a 666 hiding between 13 zeros and a 1 on either side. The ominous number can be abbreviated as 1 0(13) 666 0(13) 1, where the (13) denotes the number of zeros between the 1 and 666. Although he didn't "discover" the number, scientist and author Cliff Pickover made the sinister-feeling number famous when he named it after Belphegor (or Beelphegor), one of the seven demon princes of hell. The number apparently even has its own devilish symbol, which looks like an upside-down symbol for pi. According to...

A previously unnoticed property of prime numbers seems to violate a longstanding assumption about how they behave. o 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...

The 22 million digit number and the amazing maths behind primes January 21, 2016 by Steve Humble, The Conversation Primes: here be magic. Credit: Shutterstock It is a quite extraordinary figure. Dr Curtis Cooper from the University of Central Missouri has found the largest-known prime number - written (274207281)-1. It is around 22m digits long and, if printed in full, would take you days to read. Its discovery comes thanks to a collaborative project of volunteers who use freely available software called GIMPS (Great Internet Mersenne Prime Search) to search for primes. A number which can only be divided by...

The great mystery since the NSA and other intelligence agencies’ cyber-spying capabilities became watercooler fodder has not been the why of their actions, but the how? For example, how are they breaking crypto to decode secure Internet communication? A team of cryptographers and computer scientists from a handful of academic powerhouses is pretty confident they have the answer after having pieced together a number of clues from the Snowden documents that have been published so far, and giving the math around the Diffie-Hellman protocol a hard look. The answer is an implementation weakness in Diffie-Hellman key exchanges, specifically in the...

It is one the oldest mathematical problems in the world. Several centuries ago, the twin primes conjecture was formulated. As its name indicates, this hypothesis, which many science historians have attributed to the Greek mathematician Euclid, deals with prime numbers, those divisible only by themselves and by one (2, 3, 5, 7, 11, etc.). Under this assumption, there exists an infinite number of pairs of prime numbers whose difference is two, called twin primes (e.g., 3 and 5), but nobody has been able to confirm this so far.

 Most mathematicians have a sense that the twin primes conjecture should be true — the positioning of the prime numbers appear to be more or less random, even though on average the gaps between primes get larger, and if one has an infinitely long list of random odd numbers, we should have an infinite collection of pairs in our list. If at some point, prime numbers are always more than two numbers away from each other, we have a non-random aspect to their distribution that goes against this intuition.

Hypothesis: All odd numbers greater than one are prime Proofs: Engineer: 3, 5, 7, YES! Physicist: 3, 5, 7, [experimental error], 11, 13, [experimental error], 17, 19. [grant runs dry.] At the 95% confidence level and within the limit of experimental error, we cannot reject the hypothesis that all odd numbers greater than one are primes. Accountant: What do you want them to be? Mathematician: Before we can answer that question we need to define a Galois field of positive integers and then over that field specify an operation, factorization such that for any member of the field, the operation...

In a recent study, Bartolo Luque and Lucas Lacasa of the Universidad Politécnica de Madrid in Spain have discovered a new pattern in primes that has surprisingly gone unnoticed until now. They found that the distribution of the leading digit in the prime number sequence can be described by a generalization of Benford’s law. In addition, this same pattern also appears in another number sequence, that of the leading digits of nontrivial Riemann zeta zeros, which is known to be related to the distribution of primes. Besides providing insight into the nature of primes, the finding could also have applications...

The Great Internet Mersenne Prime Search (GIMPS)is possibly the oldest distributed computing project in existence, and has mostly existed on the fringe of the mainstream distributed computing world. Part of this is likely due to the hardcore nerdiness factor of the project. Most people aren't interested in finding huge prime numbers, as potentially useful as they might be. They'd rather fold proteins, search for little green men, or look for spinning neutron stars—all of which have a more tangible appeal than what appears to be numbers for numbers' sake. There are reasons to look for Mersenne primes, though. There are...

The Prime Number Shitting Bear