A résolu

Check p = 4n +/- 1, the generic formula for odd prime numbers
Problem statement For all odd prime number p, there exists a positive integer n, such that p = 4n +/- 1 : Check this f...

8 mois il y a

A résolu

Linear primes p' = mp + n
Problem statement List the prime numbers of the form p' = mp + n for a given (m,n) couple and such that p' < k, k positive in...

8 mois il y a

A résolu

List the twin prime couples
Problem statement The twin prime couples (p,p') are the ones such that p' = p + 2. For a given integer n > 1, list the twin p...

8 mois il y a

A résolu

Check Legendre's conjecture
Context and problem statement Legendre's conjecture states for a given positive integer n, there always exists at least one pri...

8 mois il y a

A résolu

Check Bertrand-Chebyshev's theorem about prime numbers
Historical context Bertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory ...

8 mois il y a

A résolu

List primes which are the sum of two consecutive lower primes plus minus one
Problem statement Some prime numbers can be written as the sum of two consecutive lower primes plus / minus one : Like t...

8 mois il y a

A résolu

Determine if LTI system with feedback control is stable
Linear timeiinvariant systems can be represented by the differential equation , where is an matrix, is an vector representing...

8 mois il y a

A résolu

List the near-square primes, p = n² + 1 (Landau's 4th problem)
Historical context At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime...

8 mois il y a

Problème

Determine whether a number is a seesaw number
Cody Problem 60957 dealt with balanced primes. In that case, balance was measured in terms of the average of primes around a giv...

9 mois il y a | 1 | 5 solveurs

A résolu

Chek the Delta = 6k gap theorem about arithmetic progressions in the prime number set
Context In the prime numbers set there are some arithmetic progressions (sequences of three or more consecutive prime number...

9 mois il y a

Problème

List balanced primes
A balanced prime of order is one that equals the average of the primes before it and the primes after it. For example, 79 is ...

9 mois il y a | 3 | 5 solveurs

A résolu

Baye's theorem on conditional probability
Let the given probabilities Compute the output probability

9 mois il y a

Problème

List mean-of-2 primes
The prime number 53 is the average of the first prime before it (47) and the first prime after it (59), and the prime number 11 ...

9 mois il y a | 4 | 6 solveurs

A résolu

My wife's logic
Its is always the opposite of the causality law, that is to say the implication relationship in math/logic terms : Figure...

9 mois il y a

Problème

List even numbers whose Goldbach partition does not use the largest prime
The strong Goldbach conjecture says that every even number greater than 2 can be expressed as a sum of two prime numbers—that is...

9 mois il y a | 1 | 6 solveurs

A résolu

Extra colors
Context In the RGB color system used by Matlab, the color is a 1 x 3 / row vector [R G B] with each value/component R, G, B in ...

9 mois il y a

Problème

Find the longest runs of primes generated by polynomials
Cody Problems 60942, 60943, and 60944 involve polynomials that generate primes. No polynomial can generate only prime numbers, b...

9 mois il y a | 2 | 7 solveurs

A résolu

Check the integers decomposition conjecture
Problem statement A conjecture (I rediscovered ?) related to Goldbach's one states that every integer above 2 can be written ...

9 mois il y a

A résolu

Check the 'golden prime squares' equation
Historical context In december 2023, I / Nicolas Douillet was working on prime squares properties and I found* the formula : ...

9 mois il y a

A résolu

Euclid primes
Historical context Euclid, the greek mathematician proved at his time that the prime numbers set is an infinite. By the way he ...

9 mois il y a

A résolu

Fermat primes
Historical context The french mathematician Pierre de Fermat found the formula to find some prime numbers. He thought / co...

9 mois il y a

Problème

Compile evidence for the Carmichael totient conjecture
The totient function counts the positive integers up to that are relatively prime to . The Carmichael totient conjecture state...

9 mois il y a | 2 | 4 solveurs

A résolu

Ulam primes first formula
Historical context The polish-american mathematician Stanislaw Ulam found the formula to give the first 760 prime numbers ...

9 mois il y a

A résolu

Ulam primes second formula
Historical context The polish-american mathematician Stanislaw Ulam found the formula to give some prime numbers not given...

9 mois il y a

A résolu

Euler primes
Historical context The great swiss mathematician Leonhard Euler found the formula to give some prime numbers. Problem...

9 mois il y a

A résolu

Primes numbers which are the difference of two consecutive cubes
Problem statement Given a positive integer n greater than 2, find the prime numbers less or equal to n and which are the diff...

9 mois il y a

A résolu

Find the first occurence of a given gap between two consecutive prime numbers
Given a gap = p' - p between the two consecutive prime numbers p and p', find its first occurence, f. For examples : If , f=...

9 mois il y a

A résolu

Frequencies of prime gaps
Given two positive integers n and , write a function which computes the frequency of the gap between two consecutive of the pr...

9 mois il y a

A résolu

Breaking up a chocolate bar
You've got a chocolate bar of size , and you want to break it up into bite-sized () pieces. How many steps are required to do th...

9 mois il y a

A résolu

The cake is a lie...
You're hosting a birthday party with a large number of screaming children. Fortunately, you have a gigantic sheet cake in front...

9 mois il y a