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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 : ...

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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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Broken Clock
Create a function that outputs t, an inputted matrix time x, in hours and minutes (hr:min) unless the time contains a five. In t...

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The Five Infection (Boss Level)
Given a 3x3 matrix A, replace: every value that is equal to five every value that is directly adjacent to a five with zero in...

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Fives Begone
Given any sentence as an input value 'sentence', turn all fives into the letter X and return the improved sentence. Also, turn a...

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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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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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Estimating Battery Backup Time for an Inverter
In a Battery Management System (BMS), estimating the backup time of a battery-powered inverter helps determine how long it can s...

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Battery Charge Rate Calculation
In a Battery Management System (BMS), the charge rate () of a battery can be calculated using the formula: where: is th...

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Battery State of Health (SoH) Calculation
In a Battery Management System (BMS), the State of Health (SoH) of a battery is an indicator of its overall condition. It is cal...

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Battery Charge Efficiency Calculation
In a Battery Management System (BMS), the efficiency of battery charging can be estimated using the formula: where: is the...

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Battery Voltage Drop Estimation
In a Battery Management System (BMS), the voltage drop (V_drop) due to the load can be calculated using the formula:V_drop=I×R ...

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Battery Discharge Time Estimation
In a Battery Management System (BMS), the estimated discharge time (T) of a battery can be calculated as: where: is the ...

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State of Charge (SoC) Estimation for a Battery
The State of Charge (SoC) of a battery represents its remaining charge as a percentage. It can be calculated using the formula: ...

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Battery Life Estimation for a Device
A battery-powered device consumes a constant current while operating. The estimated battery life (T) can be calculated using the...

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Matrix Pattern 1

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Sum all integers from 1 to 2^n
Given the number x, y must be the summation of all integers from 1 to 2^x. For instance if x=2 then y must be 1+2+3+4=10.

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Magic is simple (for beginners)
Determine for a magic square of order n, the magic sum m. For example m=15 for a magic square of order 3.

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Make a random, non-repeating vector.
This is a basic MATLAB operation. It is for instructional purposes. --- If you want to get a random permutation of integer...

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Number of 1s in a binary string
Find the number of 1s in the given binary string. Example. If the input string is '1100101', the output is 4. If the input stri...

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