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Motivation
I am working on a conjecture involving the sequence of least-prime-factors within $k$ consecutive numbers

Let $k=\sqrt{100}$.

$$[ 1, 10] = \{p_*,2,3,2,5,2,7,2,3,2\}$$
$$[81, 90] = \{3,2,p_*,2,5,2,3,2,p_*,2\}$$
$$[91,100] = \{7,2,3,2,5,2,p_*,2,3,2\}$$

I need a placeholder for a prime. I have narrowed this down to: $p_*$ and $p_{\square}$. Is there something else that would be preferred?

Edit additional info about use:

I don't need to track separate primes. I intend to do something like $90$ multichoose $k$ and when I tally the choices, I want the unknown primes to be counted as one choice.

edited Aug 13 at 12:39

Fred Kline

community wiki

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j(n), also known as g(n) or Jacobsthal's function, is the smallest number j such that for every positive integer a, at least one integer in [a+1,a+j] is guaranteed to be coprime to n. If you tie your work into things like j(P) where P is a primorial, that would suggest using letters like j or g as placeholders. Gerhard "Ask Me About System Design" Paseman, 2012.08.13 – Gerhard Paseman Aug 13 at 17:05

quid · Accepted Answer · 2012-08-13 12:20:58Z UTC

2

To use $p$ (with decoration) is quite common if the value ought to be prime (to signal this implcitly). What is less common is to use a symbol as a subscript, and the empty square seems also somewhat uncommon (in general, in that context).

For example, just $p$ or $p'$ and then $p''$ seem quite standard.
Alos using indeces is common $p_1,p_2, \dots$ .

Yet, with just $p$ or $p_1$ and so on you might have clashes of notation if for instance you want to denote $p_1,p_2, \dots$ the collection of all primes ordered by size.

To sidestep this you could use, if you need many, $p^{(1)}, p^{(2)}, \dots$ for the variables.

Also, $q$ and analogue constructions are somewhat common for a prime (though even more so for a prime power).

Finally, there is no rule to use a specific letter, you could use whatever. But, it is true that in (certain areas of) number theory it is very common to use $p$ or some modification thereof if it is a prime.

(I give this in CW mode, as there is no 'right' answer, I also flagged the question to be turned into CW mode.)

answered Aug 13 at 12:20

quid

community wiki

	I had considered $p_{0}$, but decided that would also conflict. I like the $p^{(1)}$ style although the numbers imply order. Maybe like this: $p^{(*)}$? I'll change question to CW mode to get more ideas. – Fred Kline Aug 13 at 12:29
	To just use the asterisk as a superscript would also work fine without parenthesis. It is true a numbering can suggest some ordering but it does not really have to imply something on the size. For instance, if one has a (not very small) system of linear equations the varialbles and coefficient are also indexed by numbers yet the numbers have no particular meaning. If you just have a couple of variables/placeholders to name I would go for $p'$, $p''$, $p^{\ast}$ and alike, but if ever you need arbitrarily many I'd suggest the numbering. – quid Aug 13 at 12:38
	I expect I will go with $p^{}$ and if I need to square it, I could do: $(p^{})^2$. I think I'll accept this answer. – Fred Kline Aug 13 at 12:52
	@quid: "If one has a system of linear equations the variables and coefficients are indexed by numbers" is only true if one chooses to do so, and in general it certainly is not. Of course one can index a finite or countable family by a subset of the set of natural numbers and ignore the canonical ordering on the latter, but since this ordering is canonical this can be confusing. In short: if you don't need an ordered set then don't take one, and if you take a set without an ordering then don't take one which most readers will view as an ordered set. – Fred Rohrer Aug 13 at 14:08
	@Fred Rohrer: to some extent I agree, and even thought about some remark to that extent to my answer. However, I maintain that it is considerably more common to say something like: "let $a_1, \dots, a_n$ be" than "let $(a_i)_{i \in I}$ with $I$ a set of cardinality $n$ be"; even if the (implicit) order (and other structure) on the index set has no relevance whatsoever. But, yes, another option would be to use say $p^{(i)}$ where $i$ is said to be in some (unspecified) indexing-set $I$ (with apropriet cardinality). Yet, in general (there are always exceptions) I would not recommend this. – quid Aug 13 at 15:28

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Need help defining placeholders for primes.

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