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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...
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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...
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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...
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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 ...
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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...
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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...
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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...
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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...
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No Fives Permitted
Create a function that gives users an custom error message if the matrix A contains a five. The error message should say "No Fiv...
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A Fiveless Factorial
Given a positive integer x, compute its factorial y, but exclude any muliplication by five if applicable.
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Don't Sum a Five
Create a function that sums the first and last element of a muti-element vector unless the value of one of the elements is 5. Do...
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Don't Include a Five (Part Two)
Given a vector A with at least one non-five, return vector B, with all fives excluded (not replaced by zeros).
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Don't Include a Five
Given a vector A, return vector B with all 5s replaced with 0s.
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High Five!
Write a function that takes a number x and returns y = 'High Five' if x is not equal to five. Return y = 'Denied' if the number ...
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A Five Introduction
Write a function that takes a number x as an input and returns the same value as y, unless x = 5, in which case the function sho...
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Laws of motion 4
Given the initial velocity 'u', final velocity 'v' and acceleration 'a', find the distance travelled.
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Estimating Battery Lifetime Based on Load Profile and Depth of Discharge (DoD)
In a Battery Management System (BMS), the lifetime of a battery depends on various factors, including the Depth of Discharge (Do...
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Estimating the Range of an Electric Vehicle (EV)
In Electric Vehicles (EVs), the driving range is the estimated distance a vehicle can travel on a fully charged battery. The ran...
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