In[30]:=
Primorial[2]
Out[30]= Primorial[2]I have prior programming experience, I've already deduced what they do. Range[n] = {1,...,n}, Prime[n] = nth prime, Prime[{2,5}] = 2nd and 5th prime = {3, 11}.Bill Simpson said:If you are a beginner with Mathematica then you need to take the replies posted here apart, use the help system or Google to read the documentation for each function, see what each part does and how they work. Then you begin putting the pieces back together, one step at a time, until you see how the whole thing works.
What does Range[] do? Then what does Range[4] do?
What does Prime[] do? Then what does Prime[2] do?
What does Prime[{2,5}] do? What does Prime[Range[4]] do?
Finally how does all this come together in what I showed
and how does that relate to the original question?
The other primorial is the product of all primes less than or equal to n. For example, Primorial[5]=Times@@{2,3,5}.Bill Simpson said:I'm confused by your "I'm interested in the other primorial."
Is that different than what I showed? How?
Perhaps I misunderstood and made a mistake. If so then please explain what I missed.
Primorial[n_]:=Times@@Prime[Range[PrimePi[n]]]The main difference between Plot Primorial[x] and Factorial[x] in Mathematica is the mathematical function that they represent. Plot Primorial[x] calculates the product of all prime numbers less than or equal to x, while Factorial[x] calculates the product of all positive integers less than or equal to x.
To use Plot Primorial[x] and Factorial[x] in Mathematica, you can simply input the desired value of x in the function, such as Plot Primorial[5] or Factorial[10]. This will return the value of the function at that specific point.
Yes, both Plot Primorial[x] and Factorial[x] can be graphed in Mathematica. You can use the Plot function to graph the values of the function over a range of x values. For example, Plot[Factorial[x], {x, 1, 10}] will graph the factorial function from x=1 to x=10.
One limitation of using Plot Primorial[x] and Factorial[x] in Mathematica is that the input value of x must be a positive integer. Attempting to use a non-integer value will result in an error. Additionally, the value of x must be within the limits of the data type used by Mathematica, which is approximately 2.5 billion.
Yes, Plot Primorial[x] and Factorial[x] can be used in conjunction with other Mathematica functions. For example, you can use the Sum function to calculate the sum of the values of Plot Primorial[x] or Factorial[x] over a range of x values. Additionally, you can use the PlotLegends function to label the graphed functions with their respective names.