[Math] Wolfram Alpha – limiting the input X set to prime integer numbers

wolfram alpha

I was curious if I can get wolfram alpha to calculate for me the values of Y, but using only the prime integer values of X .

Currently I have the following:

solve y=x+(30/x)+1 over the integers

I would like to do something like this:

solve y=x+(30/x)+1 over the prime integers

solve y=x+(30/x)+1 over the prime numbers

http://www.wolframalpha.com/input/?i=solve+y%3Dx%2B(30%2Fx)%2B1+over+the+integers

So far I am not getting the response I want… which is X=3, and Y=14.

It's simply curiosity from my part whether I can get wolfram to do it.

Best Answer

You can find the relevant solutions with the function prime(x), which returns the $x$'th prime number and the syntax solve {y=prime(x)+30/prime(x)+1} over integers (link).

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[Math] How to input this into Wolfram Alpha

You might be able use boole, which returns $0$ or $1$ depending on whether it's argument is True or False. Thus, for $n=10$, Euler's phi function $\varphi(n)$ (which counts the number of positive integers less than and relatively prime to $n$) can be expressed as

sum boole(gcd(i,10)=1), i=1..10

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Of course, it's hard to say for sure, since you don't mention your specific application. This method of computing $\varphi(n)$, however, happens to be Wikipedia's first example application of Iverson brackets.

[Math] Input integral derivative in Wolfram Alpha

I don't think the way around this is by changing the $dt$ to $dx$. Trying alternative routes, like suggested by Shuhao Cao, ended up exceeding standard computing time through Alpha, even extending additional computation time.

If you have Mathematica, it provides greater amounts of computation time, but in the case of your posted problem, the result is clearly $\sqrt{x^2 - x + 1}$ without the use of software.

Best Answer

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[Math] How to input this into Wolfram Alpha

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