Science Forums 2

[Don Blazys]

To: The Big Dog.

The key (second) root of the equation actually must be transcendental in order to generate primes, and so the task of determining its exact value will indeed be equal to, and perhaps even much more difficult than the determination of the primes themselves. The sequence of primes appears to be utterly unpredictable, so the real challenge here is to at least determine whether or not there even exists some number such as;

2.566543832171388844467529...

that can possibly be defined by some equation, series, or algorithm, because that would imply an underlying predictability.

There are also many, many other "Blazys constants" such as:

2.313036736... and 2.794019072...

that also generate the entire sequence of primes, in order of magnitude by applying different methods and/or rules. (In the above two examples, we simply subtract the whole number part, then take the reciprocal of the result.)

Proving that all such "Blazys constants" are not definable is probably impossible, so all we are left with is the possibility of trying "this, that and the other thing", just to see how far into the primes some particular "possible definition" of a "Blazys constant" will take us.

The formula in my previous post happens to generate all the primes up to and including 59, and is therefore, at present, the "world record" for a "true prime generating function". (One that does not involve sieves, comparisons or "Wilsons theorem").

At present, all known formulas such as the one in this thread are merely "curiosities" or "curios", but as I happen to take great delight in discovering them, I will continue to try "this, that and the other thing", in my spare time, if only for the fun of it.

As I said before, the probability that such a formula even exists is quite likely to be zero, but if by some miracle a really promising one is ever found, then it will indeed represent a major breakthrough.

Before I discovered the "cohesive terms" that are discussed in the thread "A Mathematical Emergency", I really didn't believe that it was algebraically possible to prevent cancelled variables from being "crossed out", or in any such "mathematical miracle".

Now I do.

Don.