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List Ormiston prime pairs
The numbers 1913 and 1931 form the first Ormiston prime pair. The numbers are consecutive primes, and they are anagrams of each ...

4 months ago

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Determine whether a number is a Ludic prime
Ludic numbers are formed by a sieve. Start with a list of the positive integers. Skip 1 and start with 2. Then delete every seco...

4 months ago

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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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List primes of the form xy+z
Consider three consecutive integers , , and . When is the number prime? For example, if or , then the results are 17 and 37, ...

4 months ago

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Compute the number of squares a knight can reach after n moves
Several Cody problems involve knights from chess. They have asked players to find a knight’s tour in a matrix (CP 96), determine...

4 months ago

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Express numbers as the sum of a prime, a square, and a cube
While traveling on an interstate highway, I noticed a sign that gave distances to three places. The distances were 3, 8, and 9 m...

4 months ago

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Find the closest geyser prime
My wife and I celebrated our honeymoon and our recent anniversary in Yellowstone and Grand Teton National Parks. After returning...

4 months ago

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List composite numbers that do not contain their prime factors as substrings
The number 63 has the prime factorization 3, 3, and 7, and it contains one of them (3) as a substring. In contrast, the number 4...

4 months ago

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Count the primes resulting from changing one digit of a number
If you start with the number 24 and seek primes by changing a single digit, you can find two: 23 and 29. If you start with 130, ...

4 months ago

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Create a vector whose elements depend on the previous element
The idea is to create a vector A whose elements depend on the previous element : *A(i+1) = 2*A(i)+1* *2 Inputs*: - A : The...

4 months ago

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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...

4 months ago

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Find the closest canyon prime
My wife and I celebrated our honeymoon and most recent anniversary in Yellowstone and Grand Teton National Parks. After returnin...

4 months ago

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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 ...

4 months ago

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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 ...

4 months ago

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Project Euler: Problem 7, Nth prime
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the Nth prime numb...

4 months ago

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Prime factor digits
Consider the following number system. Calculate the prime factorization for each number n, then represent the prime factors in a...

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

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

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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

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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 ...

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

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 ...

4 months ago

Solved

List the segmented numbers
The sequence of segmented numbers begins 1, 2, 4, 5, 8, 10, 14, 15, 16. Notice that none of the terms is the sum of consecutive ...

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

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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

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

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