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