Questions tagged [primes]
Primes or prime numbers are numbers which are divisible only by themselves and one, starting with 2, 3, 5, 7, 11.... They are commonly used in encryption and hashing algorithms.
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Find the smallest semiprime satisfying a bunch of conditions
The purpose of this code is to find the smallest semiprime \$s = a b\$ satisfying a bunch of conditions stated in the Math.SE question What is the smallest "prime" semiprime?. The conditions ...
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Java: counting letters FROM A fractal algorithm shows prime number patterning
This example finds all "letter" structures.
letter a = LMLMMM
letter b = LMMMMM
letter c = MMLMMM
letter d = MMMMMM
Symbol L = live = prime candidate number
Symbol M = multiple = composite ...
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Java: prime number envelopes FROM A fractal algorithm shows prime number patterning
It implements prime number envelopes (page 3) from my paper: https://zenodo.org/records/16829092
The full working example is on github: https://github.com/cerebrummi/primeenvelopes
"StartFA"...
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Java: A fractal algorithm shows prime number patterning
The fully working example finds all primes (theoretically). In real life the FA is constrained by stack size. The theoretical run is important, because it proves that all primes have a deterministic ...
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Prime number finder below the limit specified
Is this an optimal solution? I doubt it is. Can someone please critique my code?
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Computing π(x): the combinatorial method
This is my C++ implementation of Computing π(x): the combinatorial method by Tomás Oliveira e Silva. The math involved is elementary number theory, but fiddly and not the focus here. I have ...
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Optimizing sieving code for the Multiple Polynomial Quadratic Sieve
I wrote code for the multiple polynomial quadratic sieve (MPQS) here:
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Simple Sieve of Eratosthenes
I've implemented this version of the Sieve of Eratosthenes in Rust, with inputs. I'm mostly pleased with it, but want to know if the input logic can be simplified, and if the sieve itself can be ...
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What is the most efficient way to figure out if a single number is prime for numbers from 2 up to 2,147,483,647 in Java?
As Java programmers, we can always use the BigInteger isProbablePrime() method or store manually all prime numbers in a HashMap. This question is about the most efficient way to figure out if a single ...
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Project Euler 127 - abc-hits
Problem (Rephrased from here):
The radical of \$n\$, \$rad(n)\$, is the product of distinct prime factors of \$n\$. For example, \$504 = 2^3 × 3^2 × 7\$, so \$rad(504) = 2 × 3 × 7 = 42\$.
We shall ...
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Optimizing SymPy Implementation of prime factorization in form of QUBO
I'm trying to reproduce a paper on Prime Factorization. This paper converts the problem into a QUBO form, which then we can map it to an Ising Minimizer. I've basically done everything and I've ...
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Count how many numbers in a range have exactly three divisors
The challenge
Given array a of n numbers, I need to count how many positive numbers less than each aᵢ have exactly 3 divisors.
Constraints
1 <= aᵢ <= 2.5 * 10¹³
In other words,
the minimum ...
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Optimal Solution for the Four Divisors Problem on LeetCode
I recently encountered the Four Divisors problem on LeetCode and managed to achieve a 100% beat rate with my solution. I'd like to share it with you all and gather feedback on its effectiveness and ...
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Miller-Rabin implementation is very slow
I implemented the Miller-Rabin-Primetest in python3. But I have the feeling it is very slow. I know that there are faster version in gmpy2 package, but I want to compare it with another code I have in ...
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Miller-Rabin prime test
I have an implementation of the Miller-Rabin prime test, coded in Python 3.
I want to use that as a comparison to a prime test which I coded myself.
Unfortunately I have no idea how "fast" ...
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Construct a performant sieve of Atkin in Rust
I have implemented the sieve of Atkin in Rust. It can find all primes till 1,000,000,000 in 4.5 s using 34.4 MiB on my 1.4 GHz machine. This is a direct implementation (with some optimisations made ...
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C code for finding prime numbers
I have created a program to find prime numbers up to the 32nd power of 2. It uses the sieve of Eratosthenes. I would appreciate it if you could let me know any bugs or improvements I can make.
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Project Euler 10(Python) | Summation of Primes
This is my Python3 code which solved the 10th problem of Project Euler. I haven't passed the last 2 time limit test cases.
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Project Euler 60: Prime Pair Sets
Project Euler Prime Pair Sets:
The primes 3, 7, 109, and 673 are quite remarkable. By taking any two primes and concatenating them in any order the result will always be prime.
For example, taking 7 ...
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Find perfect and amicable numbers
I've been playing with perfect, amicable and social numbers lately, and created a class for investigating these. At present, it has functions to return the perfect and amicable numbers in a specified ...
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Miller-Rabin Primality Test in Python
I have the following implementation of the Miller-Rabin test in Python:
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Performance of Haskell prime sieve
I have this code, which is a pseudo-Sieve of Eratosthenes for generating primes:
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Hunting for the 100,001st prime in Rust
Most of my programming experience is in Python, but my first language was C, and I was intrigued by the combination which Rust offers: a streamlined syntax and no manual memory management, but with ...
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generate prime factors via wheel factorization
I want to factor random values of n that range from uint.MinValue to uint.MaxValue as ...
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Prime sieve in Rust
Using Sieve of Eratosthenes, I created a function that returns a vector of primes up to given limit.
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Make an image where pixels are colored if they are prime
This code creates a black-and-white image of variable size where the n-th pixel is white if n is a prime number and black if it isn't. It works, but I wonder if it is well written or if it could be ...
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Find factor pairs of an integer in Rust
I'm trying to efficiently generate all pairs of factors of a number n.
For example, when n=27, the factor pairs are (1, 27), (3, 9), (9, 3), (27, 1)
The order in which the pairs are found is not ...
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Strong Goldbach Conjecture with set implementation
I have devised my own version for a Goldbach verification project which uses sets to compare already sieved primes. My implementation also uses generators to "sieve a segment" since storing ...
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Prime factorization algorithm by using the multiprocessing module of Python
I may introduce a Python code of prime factorization which is from my personal project that I'm working on.
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Numpy segmented Sieve Of Eratosthenes
For the segmented Sieve Of Eratosthenes, I have devised the following code provided. And I understand that it is not the best implementation; However, it should be much quicker than what it is now. ...
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Find primes using Wilson's Theorem
The following code is an instantiation of wilson's theorem. It uses a simple factorial and division theorem to check for primality. My issue is with the performance of the code, and there are two most ...
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Möbius function using iterators for prime factors
While working on Project Euler, I have come across a few questions involving usage of the little omega function, big omega function, and Möbius function.
My prior code wrote factors into an array and ...
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Multithreaded segmented Sieve of Eratosthenes
I am fairly new to Rust and thought a good way to practice would be to write a multithreaded segmented Sieve of Eratosthenes. It performs ok (searches ten-billion numbers in about 11 seconds on my ...
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Euler's totient function for large numbers
I made this algorithm to compute Euler's totient function for large numbers. A sieve is used.
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Prime sieve for large numbers
I state that I am not an expert and that certainly the code can be improved.
I made this prime number sieve to be able to handle large numbers.
The basic idea is to write a number p=r+bW*k where r is ...
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Find factors of a Mersenne number
On RosettaCode I found this C++ version of modPow (compute 2ᵖ mod n) to find the factors of a Mersenne number.
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Next level Improved Sieve of Eratosthenes
This is the next development for the Sieve of Eratosthenes algorithm, where all the multiples of 2,3 and 5 are eliminated, which will not take any memory or time.
As my last question Improved Sieve of ...
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Improved Sieve of Eratosthenes
How can I get to a perfect coding for this algorithm?
I made the mathematical theorem, which is a development of the Sieve of Eratosthenes algorithm. I might use some help in coding.
You can find the ...
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Project Euler #51: "Prime digit replacements" in Rust
Problem: https://projecteuler.net/problem=51
"Find the smallest prime which, by replacing part of the number (not necessarily adjacent digits) with the same digit, is part of an eight prime ...
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Fast way to compute a^d mod n
For a Miller-Rabin primality test I need a fast way to compute a^d mod n.
Where a is one of 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...
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Calculate the first largest factor of 600851475143
ٍProblem description:
The prime factors of 13195 are 5, 7, 13 and 29. Largest prime factor 13195 is 29.
What is the largest prime factor of the number 600851475143 ?
Prime Factor:
any of the prime ...
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Count SemiPrimes task from Codility
I'm trying to solve the following exercise from Codility:
A prime is a positive integer X that has exactly two distinct
divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and
13.
A ...
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Clojure Prime Numbers from 1 to 1000
I am a beginner to Clojure and I made a little script that prints out every prime number from 1 to 1000. Let me know if there are any improvements that I can make:
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A simple JavaScript function that does prime factorization
This is a simple JavaScript function that does prime factorization.
I wrote it on an Android phone with online editor (I don't have access to computers in night time):
Code:
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Find prime numbers
I wanted to create a program that lists all prime numbers to a given upper bound and that will also provide the amount of primes in the set. After many hours of trial and error I was able to solve it.
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Prime number generator in lisp
My implementation is based on the incremental prime sieve described on Wikipedia. I'm relatively new to lisp so I would appreciate any comments on my coding style or on the algorithm.
The below code ...
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C code for discovering numbers with interesting/beautiful/symmetric properties
Below is a C code that generates 1000 random positive integers, for each number we check primality, palindromic property, and the square root of the sum of the digits. The purpose is to find/discover ...
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Factor 999999 numbers as fast as possible
My code finds the prime factorization of numbers, ordering the prime numbers from least to greatest.
It prints a list of 999999 prime factorizations (which can be changed if you edit the function call ...
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Sieve of Eratosthenes in F#
after looking at the pseudocode for the Sieve of Eratosthenes on wikipedia I tried implementing a similar version using F#. The code runs just fine, that is, it returns all prime numbers up until a ...
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Prime numbers iterator
I am not familiar with iterators. I am confused with the traits approach and the traditional one. I don't know which one I should use in 2021.
I wrote a minimal ...
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