Solving for Prime Numbers: Find p and d

In summary, The task is to find a number p and an integer d>2 such that p, p+d and p+2d are all prime. The suggested approach is to guess values of d and check small values of p. It is recommended to choose an even value for d. The example given is d=4 but d=2 is a simpler option, although it does not meet the requirement of being greater than 2.
  • #1
Fairy111
73
0

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.
 
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  • #2
You could just guess, of course. Guessing works quite well on this problem.
 
  • #3
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.
 
  • #4
yes, i see why d needs to be even. Cheers, il just try guesssing. Just didnt know if there was a more mathematical way that i was supposed to go about it.
 
  • #5
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.

d= 2 is simpler.
 
  • #6
HallsofIvy said:
d= 2 is simpler.

But 2 isn't bigger than 2.
 

What are prime numbers?

Prime numbers are positive integers that are only divisible by 1 and themselves. Examples include 2, 3, 5, 7, 11, etc.

How do I determine if a number is prime?

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.

What is the equation for solving for prime numbers?

The equation for solving for prime numbers is p = 2d + 1, where p is the prime number and d is any positive integer.

Can any number be expressed as a sum of two prime numbers?

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.

Why are prime numbers important in mathematics?

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.

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