All Questions
298
questions
13
votes
12
answers
2k
views
Odds for second smallest prime factor
Given a prime number \$p\$ output the asymptotic density of the set of positive integers which have \$p\$ as their second-smallest distinct prime factor
Input/Output
Input: one of the following ...
10
votes
6
answers
945
views
Unnecessary Fluff
Following the great advice (what do you mean it's not advice?!) on Adding unnecessary fluff we can devise the following task:
Take a list of positive integers and a positive integer \$m\$ as input.
...
8
votes
20
answers
1k
views
Piecing Paired Primes
Problem
You've stumbled upon a paradoxical mathematical phenomenon related to prime numbers. Consider the following scenario:
You have an infinite list of prime numbers: $$2, 3, 5, 7, 11, 13, 17, 19, ....
8
votes
8
answers
404
views
Near miss prime multiples
This challenge was originally posted on codidact.
Given a number \$n \geq 3\$ as input output the smallest number \$k\$ such that the modular residues of \$k\$ by the first \$n\$ primes is exactly \$\...
11
votes
12
answers
1k
views
The all-high powerful numbers
We've had powerful numbers, yes, but what about highly powerful numbers?
Highly powerful numbers
Let \$n\$ be a positive integer in the form
$$n = p_1^{e_{p_1}(n)}p_2^{e_{p_2}(n)}\cdots p_k^{e_{p_k}(n)...
6
votes
19
answers
2k
views
Number of bits needed to represent the product of the first primes
Input
An integer \$n\$ greater than or equal to 1.
Output
The number of bits in the binary representation of the integer that is the product of the first \$n\$ primes.
Example
The product of the first ...
23
votes
31
answers
3k
views
Is this a powerful number?
A powerful number is a positive integer \$n\$ such that for every prime \$p\$ that divides \$n\$, \$p^2\$ also divides \$n\$. Or equivalently, \$n\$ is powerful if and only if it can be written in the ...
-3
votes
7
answers
1k
views
Straight pen strokes for Prime Numbers
Challenge
You are supposed to output the series I recently designed which goes as follows which are pen stroke counts of ascending prime numbers:
...
14
votes
7
answers
1k
views
Gödel encoding - Part II (decoding)
Part I
Previous part was considered encoding of non-empty nested lists with a positive integer.
Reminding the coding procedure \$G(x)\$:
If \$x\$ is a number, \$G(x) = 2^x\$
If \$x\$ is a list \$[n_0,...
31
votes
18
answers
3k
views
Gödel encoding - Part I
Related but different.
Part II
Taken from the book: Marvin Minsky 1967 – Computation:
Finite and Infinite Machines, chapter 14.
Background
As the Gödel proved, it is possible to encode with a unique ...
16
votes
7
answers
2k
views
How Super is this Prime?
A super prime is a prime whose index in the list of primes is also a prime:
...
15
votes
19
answers
2k
views
Sophie Safe primes
Description
Write a program or function that takes in a positive integer \$n\$ as input and outputs all Sophie Germain primes that are safe primes less than or equal to \$n\$. A prime number \$p\$ is ...
15
votes
16
answers
2k
views
Imtiaz Germain Primes
Description
"Imtiaz Germain primes" is not a technical name in Mathematics, but my weird creation, in the memoir of the famous mathematician Sophie Germain. These primes can be generated by ...
12
votes
18
answers
645
views
Primes with Distinct Prime Digits
There are 18 primes with distinct prime digits (A124674). Namely, they are:
\$2, 3, 5, 7, 23, 37, 53, 73, 257, 523, 2357, 2753, 3257, 3527, 5237, 5273, 7253, 7523\$
Your task is to output this ...
5
votes
15
answers
786
views
Shortest code to generate a list of prime numbers within a given range
Strangely never asked before, this question pertains to the generation of a list of prime numbers within a given range using the shortest possible code. Several algorithms, such as the Sieve of ...