Online primitive root modulo n list or tool?

Question

Online primitive root modulo n list or tool?

2.3k Views Asked by Bumbble Comm At 29 Mar 2026 - 6:30

Please does somebody know of an online list or tool (if possible server side, not a Java applet running in my computer) to calculate the primitive roots modulo n, for instance $n \in [1,1000]$ (apart from the Wikipedia list)?

I know this site (link) which is very good, but it just calculates the primivite roots modulo a prime number, and I would like to check it for other values (if I am not wrong $n = 4, p^k$ and $2p^k$ where p is an odd prime would also have primitive roots modulo n).

I have been searching in the old questions, but I did not find it. If this was already asked I will remove the question. Thank you!

UPDATE:

Thank you very much for the code in the answers! I have made also my own Python code, but I would like to know if there is an online list or tool, it could be helpful for somebody else. Here is my (very brute force) version:

from sympy import is_primitive_root
def prim_root_prod(value):
    prlist = []
    for i in range (1,value):
        if is_primitive_root(i,value):
            prlist.append(i)
    return prlist

Original Q&A

There are 2 best solutions below

Bumbble Comm On 15 May 2015 - 5:27

These are primitive roots for the numbers that have them in $[1,2000]$. This list is a list of pairs $(n,r)$ with $n$ a number and $r$ a primitive root, the smallest one.

I got this with the following Mathematica code:

Cases[{#, PrimitiveRoot[#]} & /@ Range[2, 2000], {_, _Integer}]

**Bumbble Comm** · Accepted Answer

I don't have an online tool, but what you want seems to be the example from OEIS A046147. You might be able to tweak the Mathematica example and send it through WolframAlpha.

I give an example in the documentation for perl/ntheory for constructing that table. There's no online way to run it (that I know of) but just in case you want it:

use ntheory qw/:all/;
foreach my $n (1..1000) {
  if (!znprimroot($n)) {
    say "$n -";
  } else {
    my $phi = euler_phi($n);
    my @r = grep { gcd($_,$n) == 1 && znorder($_,$n) == $phi } 1..$n-1;
    say "$n ", join(" ", @r);
  }
}

All these functions are available in Pari/GP so it should be easy to do something similar with it.

Online primitive root modulo n list or tool?

There are 2 best solutions below

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