Sage-Tips

What is the algorithm for finding prime numbers?

In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the first prime number, 2.

What are two algorithms for finding prime numbers?

Fastest Algorithm to Find Prime Numbers

• Overview. Prime numbers have always been an interesting topic to dive into.
• Sieve of Eratosthenes. Sieve of Eratosthenes is one of the oldest and easiest methods for finding prime numbers up to a given number.
• Sieve of Sundaram.
• Sieve of Atkin.
• Conclusion.

How many 1024 bit primes are there?

As it turns out you choose from ~2.8×10^147 primes with a 1024 bit RSA key and from about ~7.0×10^613 with a 4096 bit RSA key. Then you have up to 4.9×10^1227 possible pairs of primes.

How do you make a 1024 bit prime number?

The prime number theorem states that n / ln(n) is a good approximation of π(n) because when n tends to infinity, π(n) / (n / ln(n)) = 1. As we know that primes are odd (except 2), we can increase this probability by 2, so in average, to generate a 1024 bits prime number, we have to test 355 numbers randomly generated.

How do you generate a prime number in C++?

Prime Number Program in C++

1. #include
2. using namespace std;
3. int main()
4. {
5. int n, i, m=0, flag=0;
6. cout << “Enter the Number to check Prime: “;
7. cin >> n;
8. m=n/2;

How do you generate a prime number algorithm?

The algorithm 1 Generate a prime candidate. Say we want a 1024 bits prime number. Start by generating 1024 bits randomly. 2 Test if the generated number is prime with Miller-Rabin. Run the test many time to make it more efficient. 3 If the number is not prime, restart from the beginning.

What is the goal of a random prime number generator?

The goal is to efficiently compute very large random prime numbers with a specified bit-size. The standard method of manually implementing a random prime number generator which can generate prime values with a satisfactory level of accuracy is given as follows:

How do you find prime numbers?

You can find the full code at the end of the article. There is no pattern to find prime numbers, so how can we find primes? π (n) is the number of prime numbers ≤ n. For example π (10) = 4, because 2, 3, 5 and 7 are the only primes ≤ 10.

What is the fastest algorithm for a Mersenne prime number?

A Mersenne prime number is in the form of 2^p -1. I think that Lucas-Lehmer test is the fastest algorithm discovered for Mersenne prime numbers. And if you not only want to use the fastest algorithm but also the fastest hardware, try to implement it using Nvidia CUDA, write a kernel for CUDA and run it on GPU.

https://www.youtube.com/watch?v=yYXIm4vWJIE