Solved

Mesh the pentagon (with the minimum number of triangles)
Problem statement An pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set V,...

4 months ago

Solved

Mesh the tetrahedron
Problem statement An tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five w...

4 months ago

Solved

Mesh the cube
Problem statement : mesh the cube with quadranglar / squared faces An cube / regular hexahedron is a regular polyhedron with ...

4 months ago

Solved

Mesh the octahedron
Problem statement An octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five we...

4 months ago

Solved

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

4 months ago

Solved

Check p² = 24k + 1, p > 3, the 'golden prime squares' equation
Historical context In december 2023, I / Nicolas Douillet was working on prime squares properties and I found* the formula : ...

4 months ago

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

4 months ago

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

4 months ago

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

4 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...

4 months ago

Solved

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

4 months ago

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

4 months ago

Solved

Find the first occurence of a given gap between two consecutive prime numbers
Problem statement Given a gap = p' - p between the two consecutive prime numbers p and p', find its first occurence, f. E...

4 months ago

Solved

Prime 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...

4 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...

4 months ago

Solved

List the complementary / symetric prime couples
Problem statement For a given positive integer n, provide the prime couples (p,p') such that p + p' = 10^n. NB : a number li...

4 months ago

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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...

4 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...

4 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 ...

4 months ago

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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 : ...

4 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...

4 months ago

Solved

Chek the Delta = p' - p = 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...

4 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...

4 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...

4 months ago

Solved

List numbers that cannot be expressed as the sum of two primes
The Goldbach conjecture claims that even numbers greater than 2 can be expressed as the sum of two prime numbers. What about the...

4 months ago

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P(girl likes you | she smiled at you)
Compute the probability Given the input probabilities

4 months ago

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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...

4 months ago

Solved

Greater than before
Given an array of integers, write a function that returns elements that are greater than the one before them. For instance, ...

4 months ago

Solved

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nam

4 months ago

Solved

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num

4 months ago