Risolto

Find the Prime Factors and Divisors of a Number
Given a positive integer n, find its prime factors as well as all of its divisors. Example: n=12 has prime factors [2,2,3] and ...

6 mesi fa

Risolto

Mesh the square with triangles
Problem statement An square is a regular polygon with 4 vertices and 4 edges. A triangulated mesh T (stands for triangles he...

6 mesi fa

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Check Euler's characteristic on regular polyhedra
Problem statement Given the number of vertices and the number of faces of a given regular polyhedron, compute the number of its...

6 mesi fa

Problema

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...

6 mesi fa | 1 | 6 risolutori

Risolto

Monkey and the Peaches
A monkey picked a certain number of peaches on the first day. Each day, the monkey eats half of the remaining peaches plus one ...

6 mesi fa

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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 : ...

6 mesi fa

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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...

6 mesi fa

Risolto

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...

6 mesi fa

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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...

7 mesi fa

Risolto

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...

7 mesi fa

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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 ...

7 mesi fa

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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...

7 mesi fa

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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...

7 mesi fa

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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...

7 mesi fa

Problema

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...

7 mesi fa | 1 | 5 risolutori

Risolto

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...

7 mesi fa

Problema

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 ...

7 mesi fa | 3 | 5 risolutori

Risolto

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

7 mesi fa

Problema

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 ...

7 mesi fa | 4 | 6 risolutori

Risolto

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...

7 mesi fa

Problema

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...

7 mesi fa | 1 | 6 risolutori

Risolto

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 ...

7 mesi fa

Problema

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...

7 mesi fa | 2 | 6 risolutori

Risolto

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 ...

7 mesi fa

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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 : ...

7 mesi fa

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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 ...

7 mesi fa

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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...

7 mesi fa

Problema

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...

7 mesi fa | 2 | 4 risolutori

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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 ...

7 mesi fa

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

7 mesi fa