Prime Explorer

http://primes.io/

by MrBra • 11 years ago

96 19 11 years ago

primes.io

radiodario• 11 years ago

This is awesome! thanks!

Rinum• 11 years ago

This got me 100% prime

-622x² + 1868x + 2011

kefka• 11 years ago

For the range they display, that is true.

If X = 2011, then you end up with

-2511684703, which is a factor of 2011 and (-1247104+1868+1).

orf• 11 years ago

I'm a complete novice when it comes to maths, but I have read that primes don't have any predictable order. Many better minds than me have proved this true I'm guessing, but visualizations like this seem to show at least a semblance of one. Or am I mistaken? Maybe that's what makes primes so intriguing.

jowiar2• 11 years ago

A lot of the pattern comes down to primes being relatively prime to smaller numbers, which means, for example, they're 1 modulo 2, 1 or 2 modulo 3, etc. You combine these together and find that, for example, they're all (aside from 2 or 3) going to be 1 or 5 modulo 6. Which would mean that if you lined all the numbers up in rows of 6, all primes (aside from 2 or 3) would be in the first or fifth columns.

So properties can give them a "shape", but they won't identify them.

headShrinker3• 11 years ago

I wrote a very simple tool to visualize primes in the manor you describe; shifting columns.

[link redacted]

grumpy-buffalo• 11 years ago

Primes ARE fundamentally predictable, in the following very strong sense: There is a deterministic polynomial time algorithm for checking whether a number is prime (i.e. the runtime is polynomial in the number of digits of the number being tested.) http://en.wikipedia.org/wiki/AKS_primality_test

invalid_action• 11 years ago

If we were considering weather for example we could say that the weather is predictable over a period of 1 second, somewhat predictable over a period of 1 hour, and unpredictable over a period of 1 year. It doesn't matter how much historical weather data you collect you just can't say anything about the weather over long periods of time.

If a math writer says "the primes are unpredictable" this means something like if you were given a list of all the primes between 1 and some number N then there is no way to find the next prime after N that is faster than testing the primality of N+1,N+2,... until the next one is found.

The speed of the primality test doesn't matter for predictability. It doesn't matter if I can check the current weather in 1 second or 1 millionth of a second, it doesn't help me know the weather a year from now.

But not being able to work out the next prime quickly isn't the whole story. There are many things that we can say about the whole set of primes. We do know that the next prime after N won't be much bigger than N in some sense (see Bertrand's postulate). We also know roughly how many primes there are less than a given number (Prime number theorem).

There are also many properties that exist in small sets of primes (twin prime conjecture) and the OP's visualization shows some of these. So, much like the weather, the primes are not random while still being unpredictable.

mrcactu5• 11 years ago

this app is using a lot of computing power, as evidence by my laptop fan whirring.

MrBra5• 11 years ago

Well, that's for a good cause.

TheLarch• 11 years ago

I spent countless hours on this with a pencil and calculator in the 90's, laboriously back-fitting equations via recursion. This is the fulfilment of a dream!

Also: 4x² + 570x + 20233 is 100% smooth (in the given range).

jessup• 11 years ago

Reminds me of Mills' Theorem http://mathworld.wolfram.com/MillsConstant.html

MrBra5• 11 years ago

What are those coefficients and how are they calculated?

Prime Explorer

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