Comments on: A simple recurrence that produces complex behavior — and primes!

By: Eric Rowland

Eric Rowland — Sat, 02 Aug 2008 03:25:37 +0000

I created a Demonstration to explore the recurrence, and it was recently published:

http://demonstrations.wolfram.com/PrimeGeneratingRecurrence/

You can grab the source code and play with it yourself, if you’d like.

By: Uma nova relação de recorrência geradora de números primos e 1’s demonstrada por Eric Rowland « problemas | teoremas

Thu, 31 Jul 2008 08:33:42 +0000

[...] zeta de Riemann publicados há uns anos na Internet. Adenda de 31-7-2008: Eric Rowland publicou aqui o seu próprio post (A simple recurrence that produces complex behavior — and primes!) sobre a [...]

By: Eric Rowland

Eric Rowland — Tue, 22 Jul 2008 01:14:02 +0000

Yes, you probably can’t always tell the difference. But often it’s a matter of simplicity. I think engineered objects tend to be more complex, in some sense, than objects that were found by search or just randomly written down. It’s a matter of size — the more components, the larger the space you have to search through.

In the case of prime-generating formulas, we can tell that previous formulas were explicitly constructed to generate primes because in practice they don’t generate any primes at all. So they certainly weren’t discovered (by random search) to have this property. For example, Mills’ function (http://mathworld.wolfram.com/MillsTheorem.html), as far as we can tell, requires you to explicitly put in any primes you will ever get out.

By: un1crom

un1crom — Mon, 21 Jul 2008 21:45:11 +0000

what do you mean exactly by expressly engineered for this purpose?

is there a real difference between discovery and engineering an algorithm? would you know the difference if I show you a set of engineered formula versus discovered?

Russ