Questions tagged [primes]

For challenges about identifying and manipulating prime numbers

35
votes
11answers
2k views

Prime parity peregrination

The purpose of this challenge is to graphically depict a walk on the plane, where the direction of each step \$k\$ is determined by the primality of \$k\$ and the parity of its binary expansion: ...
26
votes
16answers
948 views

Primenary Strings

A Primenary (binary-prime) string is one which, when written as a binary grid, every row and column has a prime total. That's quite a vague explanation, so let's break it down with a worked example.....
17
votes
11answers
969 views

Find the Emirps!

An emirp is a non-palindromic prime which, when reversed, is also prime. The list of base 10 emirps can be found on OEIS. The first six are: ...
23
votes
17answers
1k views

Sum pyramid of primes

Given a number N, the challenge is to get the sum of the pyramid of N primes. To clarify things, here is an example: Input: 4 We will list the first ...
25
votes
17answers
1k views

Counting +1 primes

Define that the natural number p is a +1 prime of the natural number n if p is a prime number and the standard binary representation (i.e., without leading zeroes) of p can be obtained by adding (i.e.,...
8
votes
18answers
1k views

Square-free semiprime counting

Definition A square-free semiprime is a natural number that is the product of two distinct prime numbers. The task Given a natural number n, count all square-...
190
votes
283answers
43k views

Is this number a prime?

Believe it or not, we do not yet have a code golf challenge for a simple primality test. While it may not be the most interesting challenge, particularly for "usual" languages, it can be nontrivial in ...
56
votes
103answers
11k views

List of primes under a million

This is my first code golf question, and a very simple one at that, so I apologise in advance if I may have broken any community guidelines. The task is to print out, in ascending order, all of the ...
20
votes
16answers
3k views

​Cuban​ ​Primes

Given a natural number \$n\$, return the \$n\$-th cuban prime. Cuban Primes A cuban prime is a prime number of the form $$p = \frac{x^3-y^3}{x-y}$$ where \$y>0\$ and \$x = 1+y\$ or \$x = 2+y\$ ...
36
votes
17answers
4k views

Primes other than Optimus

Challenge Given an input integer n > 0, output the number of primes (other than n, if n ...
24
votes
28answers
2k views

Magnanimous numbers

Given an positive integer as input determine if it is a magnanimous number. A magnanimous number is a number such that any insertion of a + sign between any two ...
22
votes
23answers
3k views

Find the prime factors

In this task, you have to write a program, that computes the prime factors of a number. The input is a natural number 1 < n < 2^32. The output is a list of the prime factors of the number in the ...
3
votes
10answers
377 views

Composite Factor Soup

Per the fundamental theorem of arithmetic, for a given number \$n\$, it is possible to find it's prime factors, and they are unique. Let's imagine we talk only of \$n\$ that is non-prime (composite). ...
33
votes
11answers
2k views

Encode an integer

Given positive integer n > 2. We convert it to an array as follows: If it is equal to 2 return an empty array Otherwise ...
9
votes
17answers
1k views

Primes in the prime factorisation

I saw another prime challenge coming by in PPCG, and I do love me some primes. Then I misread the introductory text, and wondered what the creative brains here had come up with. It turns out the ...
18
votes
13answers
676 views

Goldbach partitions

The Goldbach conjecture states that every even number greater than two can be expressed as the sum of two primes. For example, 4 = 2 + 2 6 = 3 + 3 8 = 5 + 3 ...
20
votes
2answers
633 views

Can a neural network recognize primes?

Background Recognizing primality seems like a poor fit for (artificial) neural networks. However, the universal approximation theorem states that neural networks can approximate any continuous ...
50
votes
18answers
9k views

The prime ant 🐜

The "prime ant" is an obstinate animal that navigates the integers and divides them until there are only primes left! Initially, we have an infinite array A containing all the integers >= 2 : ...
13
votes
9answers
1k views

Repeated Digit Primes

Another sequence, another challenge.* Definition A prime p is in this sequence, let's call it A, iff for every digit ...
26
votes
20answers
3k views

Is it a Chen prime?

A number is a Chen prime if it satisfies two conditions: It is prime itself Itself plus two is either a prime or a semi-prime. A prime is a number where it has exactly two divisors and those ...
22
votes
16answers
2k views

Sort a number's divisors by prime factorization

Given an input of an integer ≥ 2, output a list of its divisors sorted by the exponents in their prime factorizations, in ascending order, ordering first by the largest prime, then by the second ...
16
votes
16answers
1k views

Prime Powers of Primes

For the purpose of this challenge, a Prime Power of a Prime (PPP) is defined as a number that can be defined as a prime number to the power of a prime number. For example, 9 is a PPP because it can ...
32
votes
6answers
2k views

1, 2, 3, 14… or is it 15?

A well known song by the Irish rock band U2 starts with the singer Bono saying "1, 2, 3, 14" in Spanish ("uno, dos, tres, catorce"). There are various theories as to the significance of those numbers....
33
votes
37answers
4k views

Return the Closest Prime Number

Challenge This is a simple one: Given a positive integer up to 1,000,000, return the closest prime number. If the number itself is prime, then you should return that number; if there are two primes ...
26
votes
22answers
2k views

Is it a weak prime?

A prime is weak if the closest other prime is smaller than it. If there is a tie the prime is not weak. For example 73 is a weak prime because 71 is prime but 75 is composite. Task Write some ...
14
votes
9answers
3k views

Closest 7-Distinct-Prime Product

(via chat) The OEIS entry A123321 lists the sequence of numbers that are the product of seven distinct primes. For brevity, we'll call this a 7DP number. The first few numbers and their corresponding ...
34
votes
14answers
1k views

Generate n-ary numbers

A secondary number is a positive integer whose prime factors (without multiplicity) are all less than or equal to its square root. 4 is a secondary number, because ...
22
votes
28answers
2k views

Largest Prime Exponents

Given an integer n >= 2, output the largest exponent in its prime factorization. This is OEIS sequence A051903. Example Let ...
27
votes
33answers
2k views

Calculate the prime factors

We had a prime factorization challenge a while ago, but that challenge is nearly six years old and barely meets our current requirements, so I believe it's time for a new one. Challenge Write a ...
38
votes
19answers
3k views

Print the nth prime that contains n

This question will be a twist on finding the nth prime number. Challenge You must write a program that will take one input n, ...
12
votes
28answers
2k views

Array Factorization

Given an array of positive integers, output a stable array of the distinct prime factors of these integers. In other words, for each integer in the input in order, get its prime factors, sort them, ...
35
votes
34answers
3k views

Is it a Mersenne Prime?

A number is a Mersenne Prime if it is both prime and can be written in the form 2n-1, where n is a positive integer. Your task is to, given any positive integer, determine whether or not it is a ...
21
votes
14answers
2k views

Prime containment numbers (golf edition)

This is sequence A054261. The \$n\$th prime containment number is the lowest number which contains the first \$n\$ prime numbers as substrings. For example, the number \$235\$ is the lowest number ...
22
votes
21answers
3k views

Bertrand's Primes

Bertrand's Postulate states that for every integer n ≥ 1 there is at least one prime p such that n < p ≤ 2n. In order to verify this theorem for n < 4000 ...
58
votes
39answers
12k views

Find the Smoothest Number

Your challenge is to find the smoothest number over a given range. In other words, find the number whose greatest prime factor is the smallest. A smooth number is one whose largest prime factor is ...
7
votes
12answers
2k views

Shortest code to find next prime palindrome

I was trying to find the shortest code possible that given a number n, returns the next prime palindrome number (limited to below 100000). If the number itself is a prime palindrome, the code should ...
15
votes
25answers
4k views

The program that will find the next prime number

Intro: You accidentally corrupted the flow of time with a device you made for fun, that turned out to be a time machine. As a result, you got pushed to the far future. You realized that computing, ...
22
votes
19answers
2k views

Is this a consecutive-prime/constant-exponent number?

A while ago, I had a look at the prime factorization of 27000: 27000 = 23 × 33 × 53 There are two special things about that: consecutive-prime: The primes are consecutive: 2 is the ...
14
votes
27answers
2k views

Prime or highest factor

Challenge: Given an array of non-negative whole numbers numbers in the range of 0 to Infinity, Check whether all of them are primes or not. (You can take input as ...
9
votes
7answers
806 views

Golf the pseudoprimes!

Introduction / Background In a recent discussion in the crypto chat I was challenged to discuss / help with the Fermat primality test and Carmichael numbers. This test is based on the premise that <...
18
votes
21answers
1k views

Excessive Integers

For a positive integer n with the prime factorization n = p1^e1 * p2^e2 * ... pk^ek where ...
17
votes
31answers
2k views

Finding Not-Quite-Prime Numbers

Your challenge, should you chose to accept it, is to code-golf a function that returns true or false (or some similar meaningful representation of yes and no) if a number meets the following criteria: ...
12
votes
9answers
829 views

Pair-golfing Twin primes and the Collatz sequence

This is a new kind of challenge inspired by the Recover the mutated source code problem. You should write two programs or functions both in the same language. The first one should solve Task #1 and ...
17
votes
17answers
1k views

Find the smallest prime from a substring

In 1946 Erdos and Copeland proved that a certain number is a normal number, i.e. the digits in its decimal expansion are uniformly distributed. Users will input a sequence of digits and you will find ...
15
votes
33answers
3k views

Calculate the sum of the first n prime numbers

I'm surprised that this challenge isn't already here, as it's so obvious. (Or I'm surprised I couldn't find it and anybody will mark it as a duplicate.) Task Given a non-negative integer \$n\$, ...
24
votes
22answers
6k views

Can even numbers become prime?

The Sequence Everyone knows the only even prime number is 2. Ho-hum. But, there are certain even numbers n where, when ...
34
votes
13answers
2k views

Fond Memories of Past Primes

Consider a prime number p, written in base 10. The memory of p is defined as the number of distinct primes strictly less than p that are contained as substrings of p. Challenge Given a non-negative ...
25
votes
6answers
1k views

Prime containment numbers (speed edition)

This is sequence A054261 The \$n\$th prime containment number is the lowest number which contains the first \$n\$ prime numbers as substrings. For example, the number \$235\$ is the lowest number ...
6
votes
0answers
343 views

Goldbach's Comet

Back to back challenges I guess. Hopefully this one is more clear than the last. Background I was playing around with Goldbach's conjecture, and decided to plot evens (on the x-axis) vs the number ...
50
votes
43answers
5k views

Coprimes up to N

Given a number n >= 2, output all the positive integers less than n where gcd(n, k) == 1 (...