Solved

Check p = 6n +/- 1, the generic formula for odd prime numbers greater than 3
Problem statement For all odd prime number p greater than 3, there exists a positive integer n, such that p = 6n +/- 1 : ...

9 months ago

Solved

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...

9 months ago

Solved

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...

9 months ago

Solved

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...

9 months ago

Solved

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...

9 months ago

Solved

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 ...

9 months ago

Solved

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...

9 months ago

Solved

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...

9 months ago

Solved

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...

9 months ago

Problem

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 months ago | 1 | 6 solvers

Solved

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 months ago

Problem

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 ...

10 months ago | 3 | 6 solvers

Solved

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

10 months ago

Problem

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 ...

10 months ago | 4 | 6 solvers

Solved

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...

10 months ago

Problem

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...

10 months ago | 1 | 6 solvers

Solved

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 ...

10 months ago

Problem

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...

10 months ago | 2 | 7 solvers

Solved

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 ...

10 months ago

Solved

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 : ...

10 months ago

Solved

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

10 months ago

Solved

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

10 months ago

Problem

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...

10 months ago | 2 | 4 solvers

Solved

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

10 months ago

Solved

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

10 months ago

Solved

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

10 months ago

Solved

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...

10 months ago

Solved

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=...

10 months ago

Solved

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...

10 months ago

Solved

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...

10 months ago