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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."
The link isn't in the summary -- but off to the right of the title.
I've hated this "feature" of /. every since they implemented a year or so ago.
>> In base 2, every prime number is 100% likely to be followed by a prime ending in 1
That was kind of my thought too. Isn't the "9/1" thing kind of base 10-ist?
Everyone with at least a passing interest in cryptography and computer security does. Primes is basically what we rely on in these fields.
Quite seriously, every time someone comes up with a claim that something can be done "more easily", "more efficiently" or generally "faster" in a field that remotely touches on prime numbers, you can see the ripples in the fabric of spacetime from cryptographers shaking in their boots.
We used to have a Bill of Rights. Now, with the rights gone, all we have left is the bill.
Intuitively it makes sense. Assume the first H has been tossed. For Alice, she fails by tossing another H. However, this second H can be the first H of a successful HT sequence, so in failure there is a silver lining - she's halfway to success and can stop after tossing a single T. Full sequence: HHT.
For Bob, after tossing the first H, tossing a T means he has to start over. He needs to toss another H first, followed by yet another H to succeed. His task is harder. Full sequence: HTHH.
The base doesn't change what the number IS, only how it is written down.
the fact that it's extremely difficult to determine the factors of large prime numbers is the basis for a lot of cryptography
I think you might have jumbled your words.
It's exceptionally easy to determine the factors of any large prime number because there are only two; the number one the number itself. Determining the prime factors of a large, non-prime number, on the other hand, is a challenge.
The twin prime conjecture is independent of the base, so the base doesn't matter for it to be true or false.
I would find this surprising, since in a base 2 system every prime number ending in 1 is followed by a prime number ending in 1.
There are 10 kinds of people who understand binary. Those who do and those who don't.