Primes plot elbowing-in on Pi's day postulating prototypical properties
-
"Mathematicians Discover Prime Conspiracy" "A previously unnoticed property of prime numbers seems to violate a longstanding assumption about how they behave." [^]. "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." You woulda thunk there was nought left to discover about prime numbers. I think what the "9's" are doing with "1's" is disgraceful, and stinks of imperialism.
«The truth is a snare: you cannot have it, without being caught. You cannot have the truth in such a way that you catch it, but only in such a way that it catches you.» Soren Kierkegaard
-
It says more about the authors than it does about numbers. Prime numbers are prime regardless of how they're represented. Base-10 isn't the only option.
PIEBALDconsult wrote:
Base-10 isn't the only option.
And base-10 isn't the only base which demonstrates weirdness:
Quote:
Looking at prime numbers written in base 3 — in which roughly half the primes end in 1 and half end in 2 — he found that among primes smaller than 1,000, a prime ending in 1 is more than twice as likely to be followed by a prime ending in 2 than by another prime ending in 1. Likewise, a prime ending in 2 prefers to be followed a prime ending in 1. ... 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.
"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer
-
"Mathematicians Discover Prime Conspiracy" "A previously unnoticed property of prime numbers seems to violate a longstanding assumption about how they behave." [^]. "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." You woulda thunk there was nought left to discover about prime numbers. I think what the "9's" are doing with "1's" is disgraceful, and stinks of imperialism.
«The truth is a snare: you cannot have it, without being caught. You cannot have the truth in such a way that you catch it, but only in such a way that it catches you.» Soren Kierkegaard
-
It says more about the authors than it does about numbers. Prime numbers are prime regardless of how they're represented. Base-10 isn't the only option.
It isn't just the base number 10, if you read the article, you'll find that:
Quote:
Looking at prime numbers written in base 3 — in which roughly half the primes end in 1 and half end in 2 — he found that among primes smaller than 1,000, a prime ending in 1 is more than twice as likely to be followed by a prime ending in 2 than by another prime ending in 1. Likewise, a prime ending in 2 prefers to be followed a prime ending in 1.
This really appears to be related to the numbers as such, not an artefact of the decimal representation.
GOTOs are a bit like wire coat hangers: they tend to breed in the darkness, such that where there once were few, eventually there are many, and the program's architecture collapses beneath them. (Fran Poretto)
-
I love how this whole thing is presented as if the numbers are actors that actually have a say in all this - "repel" etc. Math theory as a drama or suspense novel - West End Math Story :cool:
Reminds me of a strip with a guy viewing a graph of the function y=1/x : "They say they'll meet in infinity" And the girl next to him: "How romantic" :rose:
GOTOs are a bit like wire coat hangers: they tend to breed in the darkness, such that where there once were few, eventually there are many, and the program's architecture collapses beneath them. (Fran Poretto)
-
"Mathematicians Discover Prime Conspiracy" "A previously unnoticed property of prime numbers seems to violate a longstanding assumption about how they behave." [^]. "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." You woulda thunk there was nought left to discover about prime numbers. I think what the "9's" are doing with "1's" is disgraceful, and stinks of imperialism.
«The truth is a snare: you cannot have it, without being caught. You cannot have the truth in such a way that you catch it, but only in such a way that it catches you.» Soren Kierkegaard
Quote:
Among the first billion prime numbers
This doesn't seem any more startling than getting 4 heads in a row when flipping a coin. There are an infinite number of primes, so eventually the distribution will even out.
Cheers, Mike Fidler "I intend to live forever - so far, so good." Steven Wright "I almost had a psychic girlfriend but she left me before we met." Also Steven Wright "I'm addicted to placebos. I could quit, but it wouldn't matter." Steven Wright yet again.
-
The 1's have had it too good for too long, they have it coming I tell ya.
"the debugger doesn't tell me anything because this code compiles just fine" - random QA comment "Facebook is where you tell lies to your friends. Twitter is where you tell the truth to strangers." - chriselst "I don't drink any more... then again, I don't drink any less." - Mike Mullikins uncle
I respectfully have to disagree. Everybody knows that 1 is the loneliest number.
-
Quote:
Among the first billion prime numbers
This doesn't seem any more startling than getting 4 heads in a row when flipping a coin. There are an infinite number of primes, so eventually the distribution will even out.
Cheers, Mike Fidler "I intend to live forever - so far, so good." Steven Wright "I almost had a psychic girlfriend but she left me before we met." Also Steven Wright "I'm addicted to placebos. I could quit, but it wouldn't matter." Steven Wright yet again.
Yes, they do. But according to the article, what these mathematicians were amazed at was how LONG it takes for them to even out. Much longer than their intuition would have predicted. (They were also surprised at how long it took to notice this peculiarity.)
-
It says more about the authors than it does about numbers. Prime numbers are prime regardless of how they're represented. Base-10 isn't the only option.
Perhaps you should try actually reading the article, which mentions other bases. The issue isn't the base, but that the differences between consecutive primes isn't entirely random.
-
Quote:
Among the first billion prime numbers
This doesn't seem any more startling than getting 4 heads in a row when flipping a coin. There are an infinite number of primes, so eventually the distribution will even out.
Cheers, Mike Fidler "I intend to live forever - so far, so good." Steven Wright "I almost had a psychic girlfriend but she left me before we met." Also Steven Wright "I'm addicted to placebos. I could quit, but it wouldn't matter." Steven Wright yet again.
Those are totally different things. Getting 4 heads in a row is a random outcome that is exactly as likely as getting 4 tails in a row. This discovery is about non-random patterns in the differences between consecutive primes.
