Re: prime number siteswaps

Guy G wrote:

bill coad wrote:

PinkNigel wrote:

PinkNigel wrote:

ordo.v wrote:


Can we prove that there are infinitely many prime numbers that are
vaild
siteswaps?


I suspect that would look very much like the proof that there are
infinitely many primes.
However, given that the largest known primes run to many millions of
digits, who's going to be juggling
them? (It'd make a more interesting competition than 360s, that's for
sure...)


And then another thought - If you accept that, say, 101 is valid as a 101
ball cascade, then the infinite
valid prime siteswap proof looks exactly like the infinite prime proof.
So
the whole question needs
revising with an upper limit on the number of objects.


Since the alphabet is used for digits greater than nine, 101 wouldn't be
the standard representation for a 101 ball cascade.

What would be the standard representation of a 101 ball cascade? Going
off ASCII 97 being 'a' (10), it could be ASCII 101+87 = ¼. On the PC I'm
using, that's a bit like '1/4', but I'm not sure how universal extended
ASCII is. http://asciitable.com/ seems to suggest that there are
variations of the extended character set, and actually lists a different
character for ASCII 188.

Anyway, my point was that if you wanted to represent a 101 ball cascade,
you would in fact need to write it as "101" but state what your intentions
were. Of course it does feel like cheating, mostly because it makes the
problem too easy. Not that I'm going to solve the harder one, mind you.

Guy


Comvention has been to use letters when we run out of digits at 9.
Practical limits have most ignoring what happens when we run out of 26
letters in the alphabet (English). Ed Carstens' JuggloPro program
distinguishes between upper and lower case letters, giving 52 of them.
Add 10 numerical digits and still only get a limit of 62. Sciences have
often used the Greek alphabet and similiar solutions could resolve the 101
ball pattern problem.
Point is that the number of digits or characters in the pattern represent
the period of the pattern making 101 an invalid period 3 pattern. Within
practical limits there should always be a single character available to
represent a given throw height.
Finding prime numbered patterns inherently limits throw heights to 9,
since incorporating letters to denote higher throws in patterns results in
strings that aren't defined as prime or composite numbers.


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