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Feeds
A résolu
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...
2 jours il y a
A résolu
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 jours il y a
A résolu
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...
3 jours il y a
A résolu
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...
3 jours il y a
A résolu
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...
3 jours il y a
A résolu
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 jours il y a
A résolu
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 jours il y a
A résolu
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 jours il y a
A résolu
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 jours il y a
A résolu
The Goldbach Conjecture, Part 2
The <http://en.wikipedia.org/wiki/Goldbach's_conjecture Goldbach conjecture> asserts that every even integer greater than 2 can ...
5 jours il y a
A résolu
Twins in a Window
<http://en.wikipedia.org/wiki/Twin_primes Twin primes> are prime numbers that differ by 2, such as [11,13] or [41,43]. Write a f...
5 jours il y a
A résolu
Prime factor digits
Consider the following number system. Calculate the prime factorization for each number n, then represent the prime factors in a...
5 jours il y a
A résolu
Twin Primes
Twin primes are pairs of primes that are immediately next to each other (difference of two). The lesser of twin primes are 3, 5,...
5 jours il y a
A résolu
Mersenne Primes vs. All Primes
A Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number. <https://www.mathworks.com/matl...
5 jours il y a
A résolu
Mersenne Primes
A Mersenne prime is a prime number of the form M = 2^p - 1, where p is another prime number. For example, 31 is a Mersenne prim...
5 jours il y a
A résolu
Circular Primes (based on Project Euler, problem 35)
The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime. The...
5 jours il y a
A résolu
Sophie Germain prime
In number theory, a prime number p is a *Sophie Germain prime* if 2p + 1 is also prime. For example, 23 is a Sophie Germain prim...
6 jours il y a
A résolu
Find the next prime number
Find the next prime number or numbers for given n. For example: n = 1; out = 2; or n = [5 7]; out = [7 11]; ...
6 jours il y a
A résolu
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...
6 jours il y a
A résolu
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...
6 jours il y a
A résolu
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 ...
6 jours il y a
A résolu
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...
6 jours il y a
A résolu
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 (...
6 jours il y a
A résolu
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 ...
6 jours il y a
A résolu
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...
6 jours il y a
A résolu
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 ...
6 jours il y a
A résolu
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)
6 jours il y a
A résolu
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...
6 jours il y a
A résolu
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...
environ 2 mois il y a
A résolu
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...
environ 2 mois il y a
