When I run:
plot all primes and y=x from 1 to 100
In Wolfram Alpha it shows the third quadrant, where both functions are undefined. Is this a WA glitch or an error on my part? Does anyone know how it can be fixed? Screen capture:
Sometimes, Wolfram|Alpha misunderstands your input, like in this case. You can leave feedback for the Wolfram|Alpha team on the webapage. They are always interested in seeing examples like this so they can improve the responses you get.
Your query seems ambiguous as to whether you want the first 100 primes or only those primes whose values are less than 100. I’ll assume the latter meaning.
That’s a rather complicated query you’re trying to pose to Wolfram!Alpha. Try a simpler one first—just ask for a plot of those primes. Even that is tricky to request.
You’ll get an error if you ask merely “plot primes from 1 to 100”, as Wolfram!Alpha will try to use the function Prime and evaluate it at inputs such as 1.00202, which make no sense.
“plot primes between 1 and 100 increment 1” works. (Oddly, Wolfram!Alpha says the interpretation is “plot primes between 1 and 100”!)
I don’t know, though, what additional query will add the graph of y=x to the result.
In Mathematica itself, what you ask is easy to do. One way is:
p = ListPlot[Prime[Range[100]]];
g = Plot[x, {x, 1, 100}];
Show[{p, g}]
Note that the ListPlot expression will produce a plot of the 1st through the 100th prime, that is, with an x-coordinate up to 541. However, the Plot expression restricts x to a maximum of 100.