Is there are some references to algorithms that generate the set of prime numbers located between two given numbers n₁ and n₂?

I would like to consider the cases when n₁ is large while n₂-n₁ is small or while n₂-n₁ is large.

If we consider these cases:

[1] n₁=$2^{10}$ & n₂=$2^{11}$;

[2] n₁=$2^{40}$ & n₂=$2^{45}$, (modified to [2a]);

[3] n₁=$2^{100}$ & n₂=$2^{101}$, (modified to [3a]);

[4] n₁=$2^{1000}$ & n₂=$2^{1001}$, (modified to [4a]);

Is there is a well known algorithm to generate the set of all primes p ∈ [n₁,n₂] for any of these cases without generating all primes p < n₁?

By considering for example these cases:

[2a] n₁=$2^{40}$ & n₂=$2^{40}+2^{20}$;

[3a] n₁=$2^{100}$ & n₂=$2^{100}+2^{20}$;

[4a] n₁=$2^{1000}$ & n₂=$2^{1000}+2^{20}$.

Is there are some references to algorithms that generate the set of prime numbers located between two given numbers n1 n₁ and n2 n₂?

I would like to consider the cases when n1 n₁ is large while (n2-n1 n₂-n₁ is small ) or (n2-n1 while n₂-n₁ is large).

If we consider these cases:

[1] n1=$2^{10}$ n₁=$2^{10}$ & n2=$2^{11}$; n₂=$2^{11}$;

[2] n1=$2^{40}$ n₁=$2^{40}$ & n2=$2^{45}$, n₂=$2^{45}$, (modified to [2a]);

[3] n1=$2^{100}$ n₁=$2^{100}$ & n2=$2^{101}$, n₂=$2^{101}$, (modified to [3a]);

[4] n1=$2^{1000}$ n₁=$2^{1000}$ & n2=$2^{1001}$, n₂=$2^{1001}$, (modified to [4a]);

Is there is a well known algorithm to generate the set of all primes $ p \in ∈ [n_1,n_2]$ n₁,n₂] for any of these cases without generating all primes p < n1n₁?

[2a] n1=$2^{40}$ n₁=$2^{40}$ & n2=$2^{40}+2^{20}$; n₂=$2^{40}+2^{20}$;

[3a] n1=$2^{100}$ n₁=$2^{100}$ & n2=$2^{100}+2^{20}$; n₂=$2^{100}+2^{20}$;

[4a] n1=$2^{1000}$ n₁=$2^{1000}$ & n2=$2^{1000}+2^{20}$. n₂=$2^{1000}+2^{20}$.

Is there are some references to algorithms that generate the set of prime numbers located between two given numbers n1 and n2 ?

I would like to consider the cases when n1 is large while (n2-n1 is small) or (n2-n1 is large)

If we consider these cases: [1] n1=$2^{10}$ & n2=$2^{11}$; [2] n1=$2^{40}$ & n2=$2^{45}$; , (modified to [2a]); [3] n1=$2^{100}$ & n2=$2^{101}$; , (modified to [3a]); [4] n1=$2^{1000}$ & n2=$2^{1001}$. , (modified to [4a]);

Is there is a well known algorithm to generate the set of all primes $ p \in [n_1,n_2]$ for any of these cases without generating p < n1?

[2a] n1=$2^{40}$ & n2=$2^{40}+2^{20}$; [3a] n1=$2^{100}$ & n2=$2^{100}+2^{20}$; [4a] n1=$2^{1000}$ & n2=$2^{1000}+2^{20}$.

Is there are some references to algorithms that generate the set of prime numbers located between two given numbers n1 and n2 ?

I would like to consider the cases when n1 is large while (n2-n1 is small) or (n2-n1 is large)

If we consider these cases: [1] n1=$2^{10}$ & n2=$2^{11}$; [2] n1=$2^{40}$ & n2=$2^{45}$; [3] n1=$2^{100}$ & n2=$2^{101}$; [4] n1=$2^{1000}$ & n2=$2^{1001}$.

Is there is a well known algorithm to generate the set of all primes $ p \in [n_1,n_2]$ for any of these cases without generating p < n1?

[2a] n1=$2^{40}$ & n2=$2^{40}+2^{20}$; [3a] n1=$2^{100}$ & n2=$2^{10}+2^{20}$n2=$2^{100}+2^{20}$; [4a] n1=$2^{1000}$ & n2=$2^{1000}+2^{20}$.

Is there are some references to algorithms that generate the set of prime numbers located between two given numbers n1 and n2 ?

I would like to consider the cases when n1 is large while (n2-n1 is small) or (n2-n1 is large)

If we consider these cases: [1] n1=$2^{10}$ & n2=$2^{11}$; [2] n1=$2^{40}$ & n2=$2^{45}$; [3] n1=$2^{100}$ & n2=$2^{101}$; [4] n1=$2^{1000}$ & n2=$2^{1001}$.

Is there is a well known algorithm to generate the set of all primes $ p \in [n_1,n_2]$ for any of these cases without generating p < n1?

[2a] n1=$2^{40}$ & n2=$2^{40}+2^{20}$; [3a] n1=$2^{100}$ & n2=$2^{10}+2^{20}$; [4a] n1=$2^{1000}$ & n2=$2^{1000}+2^{20}$.

Is there are some references to algorithms that generate the set of prime numbers located between two given numbers n1 and n2 ?

I would like to consider the cases when n1 is large while (n2-n1 is small) or (n2-n1 is large)

If we consider these cases: [0] 1] n1=$2^{10}$ & n2=$2^{11}$; [1] 2] n1=$2^{40}$ & n2=$2^{45}$; [2] 3] n1=$2^{100}$ & n2=$2^{101}$; [3] 4] n1=$2^{1000}$ & n2=$2^{1001}$.

Is there is a well known algorithm to generate the set of all primes $ p \in [n_1,n_2]$ for any of these cases without generating p < n1?

Is there are some references to algorithms that generate the set of prime numbers located between two given numbers n1 and n2 ?

I would like to consider the cases when n1 is large while (n2-n1 is small) or (n2-n1 is large)

If we consider these three cases: [0] n1=$2^{10}$ & n2=$2^{11}$; [1] n1=$2^{40}$ & n2=$2^{45}$; [2] n1=$2^{100}$ & n2=$2^{101}$; [3] n1=$2^{1000}$ & n2=$2^{1001}$.

Is there is a well known algorithm to generate the set of all primes $ p \in [n1,n2]$ n_1,n_2]$ for any of these cases without generating p < n1?

Is there are some references to algorithms that generate the set of prime numbers located between two given numbers n1 and n2 ?

I would like to consider the cases when n1 is large while (n2-n1 is small) or (n2-n1 is large)

If we consider these three cases:

[1] n1=$2^{40}$ & n2=$2^{49}$n2=$2^{45}$; [2] n1=$2^{100}$ & n2=$2^{120}$n2=$2^{101}$; [3] n1=$2^{1000}$ & n2=$2^{1020}$n2=$2^{1001}$.

Is there is a well known algorithm to generate the set of all primes $ p \in [n1,n2]$ for any of these cases ?

Is there are some references to algorithms that generate the set of prime numbers located between two given numbers n1 and n2 ?

I would like to consider the cases when n1 is large while (n2-n1 is small) or (n2-n1 is large)

If we consider these three cases:

[1] n1=$2^{40}$ & n2=$2^{41}$n2=$2^{49}$; [2] n1=$2^{100}$ & n2=$2^{101}$n2=$2^{120}$; [3] n1=$2^{1000}$ & n2=$2^{1001}$n2=$2^{1020}$.

Is there is a well known algorithm to generate the set of all primes $ p \in [n1,n2]$ for any of these cases ?

Is there are some references to algorithms that generate the set of prime numbers located between two given numbers n1 and n2 ?

I would like to consider the cases when n1 is large while (n2-n1 is small) or (n2-n1 is large)

If we consider these three cases:

[1] n1=$2^{40}$ & n2=$2^{41}$; [2] n1=$2^{100}$ & n2=$2^{101}$; [3] n1=$2^{1000}$ & n2=$2^{1001}$.

Is there is a well known algorithm to generate the set of all primes $ p \in [n1,n2]$ for any of these cases ?

Is there are some references to algorithms that generate the set of prime numbers located between two given numbers n1 and n2 ?

I would like to consider the cases when n1 is large while (n2-n1 is small) or (n2-n1 is large)

Is there are some references to algorithms that generate the set of prime numbers located between two given numbers n1 and n2 ?