4 comments on “A simple recurrence that produces complex behavior — and primes!

  1. 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?


  2. 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.

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

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