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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...

3 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 ...

3 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 : ...

3 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...

3 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...

3 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...

3 months ago

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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...

3 months ago

Solved

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 ...

4 months ago

Solved

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 : ...

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

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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...

4 months ago

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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

Estimating Monthly Electricity Cost for a Household Appliance
You recently bought an electric kettle for your kitchen, and you want to estimate how much it costs to run every month. The kett...

9 months ago

Solved

Voltage Divider Calculation
A voltage divider is a simple circuit used to obtain a reduced voltage from a higher voltage source using two resistors in serie...

9 months ago

Solved

LED Current Calculation
In an electrical circuit, the current (III) flowing through an LED is determined using Ohm’s Law: Where: I is the current ...

9 months ago

Solved

Inductor Energy Storage Calculation
The energy (EEE) stored in an inductor is given by the formula: Where: E is the energy in joules (J) L is the inductance in...

9 months ago

Solved

Calculate Charge Using Capacitance and Voltage
The charge (Q) stored in a capacitor is given by the formula:Q=C×V where: C is the capacitance (in farads) V is the voltage (...

9 months ago

Solved

Energy Stored in a Capacitor
The energy (E) stored in a capacitor is given by the formula: where: C is the capacitance (in farads) V is the voltage (in ...

9 months ago

Solved

Calculate Current in a Series Circuit Using KVL
Kirchhoff's Voltage Law (KVL) states that the sum of voltages around a closed loop is zero. Given a voltage source (V) and three...

9 months ago

Solved

Calculating the Total Resistance in a Series Circuit
Description: In a series circuit, the total resistance is the sum of the individual resistances. This problem asks you to write ...

9 months ago

Solved

Simple Electrical Power Calculation
Calculate the electrical power using the formula: P=V×I where: V is the voltage (in volts) I is the current (in amperes)

9 months ago

Solved

Ohm’s Law - Calculate Resistance
Ohm’s Law states that resistance R can be calculated as:R=V/I where: V is the voltage (in volts) I is the current (in ampere...

9 months ago

Solved

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...

9 months ago

Solved

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...

9 months ago

Solved

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...

9 months ago