Hi, I have a question but it is about wolfram alpha rather than mathematica so I ask just in case is still of interest and sorry for being off topic, the problem is that I'm trying to check a formula from wikipedia but I don't know how to write the mod condition it is the second expression here en.wikipedia.org/wiki/…, any help would be appreciated, thanks
@Dabed You may have better luck explaining what you want to achieve instead of sending us to read Wikipedia about it. What do you want to write and why does it need to be in Wolfram Alpha?
@rhermans thanks, I have never used it but I can access mathematica trough uni so either is fine really I only thought wolfram alpha would be enough to do it and yes probably without wikipedia it can be stated simpler equivalent problem mainly what I know to do is how to multiply the first n primes $\prod_{p \in \mathbb{P} }p$ but what I want to achieve is to multiply only those that are equal to 5 mod 6 $\prod_{p \equiv 5 \pmod{6},\atop p \in \mathbb{P} }p$
@Dabed Given that you could work on this on Wolfram Cloud or your university Mathematica, I would suggest that you articulate your question in detail by posting a formal question.
@rhermans thanks, as it seems there is no easy command I guess I will need an array and if condition which would exclude wolfram alpha and leave wolfram mathematica as my best bet, wolfram cloud sounds easier so will try signing up later with more calm and if I still not able to do it then I will ask again as a formal question, thanks again and best regards
As I understand it. @Dabed wants an "Infinite product", the problem is expressing the domain of all primes 5 Mod 6, up to infinity. Creating a table would be simple enough... `pp[n_]:=Table[With[{p=Prime[k]},If[Mod[p,6]==5,p,Nothing]],{k,1,n}]`
@rhermans I went to college for computer game development, but only spent a few years in the field before switching to regular software development. Games is too much work for the same amount of money :)
You do some math for games, of course, but most of it is very applied and a little rote. Plus I didn't have Mathematica back then to help me learn.
Once you learn to learn, there is not much need for formal courses, unless you really do not enjoy the topic and need the discipline to get through. Most likely you don't need a maths class, unless you are talking about object-oriented programming.
@Dabed Even Mathematica doesn't know how to evaluate that product, so I'm not confident Alpha knows what to do with it. For reference, here's how to represent it in Mathematica: Product[Piecewise[{{p/(p - 1), Element[p, Primes] && Mod[p, 6] == 1}}, 1], {p, 2, Infinity}] Product[Piecewise[{{p/(p + 1), Element[p, Primes] && Mod[p, 6] == 5}}, 1], {p, 2, Infinity}]
(In principle one could also use Boole[], but I find it less convenient for products than for e.g. sums or integrals.)
I suggest that people happy to see J.M. back, like I am, could consider treating him with a small ko-fi. It would be nice to chip in for the much-needed computer.
@CarlLange Sorry for the delay and thanks, yes in the first link those are the primes I'm interested in wolfram recognizes the verbal expression " first 12 primes congruent to 5 mod 6" as your wrote and also "product of first 12 numbers" but it can't with "product of first 12 primes congruent to 5 mod 6", the second link is only missing the condition of p being prime so it starts at 1 and gives p/p-1=1/0=infinity I had something similar but couldn't fix either of them.
@J.M.can'tdealwithit thanks that is the whole thing I only got to spend some time reading on arrays and signing up was a lot easier than I thought so I just used it right away and checked it with mod 4 also, it seems to confirm the second expression from wikipedia, I added the citation needed tag on it and asked the user to provide a citation or proof but it seems to have been edited with a throw-away account so I was thinking of asking on math.stack but wanted to verify it numerically first
Is it known that Normal[{Dataset[{}]}] === {{}} returns False in Mathematica 12.0, but (correctly) True from 12.1 on ? It looks to me that https://reference.wolfram.com/language/tutorial/IncompatibleChanges.html is somewhat incomplete ...
