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Fairy111
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Homework Statement
Find a number p and an integer d>2 such that p, p+d and p+2d are all prime.
Homework Equations
The Attempt at a Solution
Any help with how to go about this would be appreciated, thanks.
Dick said:Just pick a value of d and check small values of p. You'll want to pick a value of d that's even. Do you see why? I suggest d=4.
HallsofIvy said:d= 2 is simpler.
Prime numbers are positive integers that are only divisible by 1 and themselves. Examples include 2, 3, 5, 7, 11, etc.
One method is to check if the number is only divisible by 1 and itself. Another method is to use the Sieve of Eratosthenes, which involves creating a list of all numbers up to the desired number, crossing out all multiples of each prime number, and the remaining numbers are prime.
The equation for solving for prime numbers is p = 2d + 1, where p is the prime number and d is any positive integer.
Yes, any even number greater than 2 can be expressed as the sum of two prime numbers. This is known as Goldbach's Conjecture, but it has not yet been proven to be true for all numbers.
Prime numbers are important in many areas of mathematics, including number theory, cryptography, and computer science. They also have real-world applications in fields such as finance and physics. Additionally, prime numbers are the building blocks of all other numbers, making them essential in understanding the fundamental properties of numbers.