# Trying to create a list that counts the number primes for each remainder class

Considier the remainder of the first $$2500$$ prime numbers by the numbers from $$3$$ to $$30$$, included.

1. Calculate how many primes are in each remainder class. That is, create a list that for each number between $$3$$ and $$30$$, gives for each remainder class the number of primes in it. Example. the first $$5$$ primes are: $$2,3,5,7,11$$. If we consider the remainders by $$3$$, we have: $$2,0,2,1,2$$. That is: $$1$$ with remainder $$0$$; $$1$$ with remainder $$1$$ and $$3$$ with remainder $$2$$.

I am having trouble condensing my program because I need to create a list for each number between 3 to 30. How could I add the remainders $$3$$ to $$30$$ to my program before it counts how many primes are in each remainder class.

I shortened just to see what is happening (ie. I shortened $$2500$$ to $$5$$)

list = Sort[Flatten[Table[n, {n, 1, 5}]]];
PrimeQ[list];
primelist =
Length[Select[list, PrimeQ]] ;
divide = Mod[Total /@ list, 3];
remainder2 = Count[divide, 2]
remainder1 = Count[divide, 1]
remainder0 = Count[divide, 0]


results were:

    {2, 3, 5, 7, 11}
{True, True, True, True, True}
3
1
1


n = 2500;
m = 21;
primes = Prime[Range @ 2500];

Counts[Mod[primes, #]] & /@ Range[3, m] // Column If you wish you can reorganize the information above into a Dataset:

KeyMap[ToString] /@ KeySort /@ KeyUnion[Counts[Mod[primes, #]] & /@ Range[3, m]] //
MapIndexed[Join[Association["m" -> ToString[#2[] + 2]],
Association["remainderClass" -> #]] &] // Dataset 