Solving for Prime Numbers: Find p and d

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Homework Help Overview

The problem involves finding a prime number p and an integer d greater than 2, such that p, p+d, and p+2d are all prime numbers. The context is within number theory, specifically focusing on properties of prime numbers.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss guessing values for p and d, with suggestions to choose an even value for d. There is a mention of trying specific values and checking for primality.

Discussion Status

Some participants have offered suggestions for values of d, noting that d should be even. There is acknowledgment of the simplicity of certain choices, but no consensus on a definitive method or solution has been reached.

Contextual Notes

There is a constraint that d must be greater than 2, which has led to some confusion regarding the selection of values. Participants are exploring the implications of these constraints on their approaches.

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.
 
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You could just guess, of course. Guessing works quite well on this problem.
 
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.
 
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.
 
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.
 
HallsofIvy said:
d= 2 is simpler.

But 2 isn't bigger than 2.
 

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