Problem...

enzocreti · 2020-02-23, 22:17

1763=5879-4423+307

1763 can be written as x-y+z
Where x y z are primes

Are there other primes x y z such that

1763=x-y+z?

Every integer can be written as x-y+z with x y z primes?

Are there others primes x y z such that
1763=x-y+z?

Dylan14 · 2020-02-23, 23:47

An easy way we could do this would be to fix one of the values of x, y and z to a particular prime. For example, let's take z = 53, which is prime.
Then your equation becomes
1763 = x - y + 53, or
1710 = x - y
which implies y = x - 1710. So we merely need to seek solutions where x and x - 1710 are prime. Using the following Mathematica code

Code:

For[x = 1711, x <= 3000, x++, 
 If[PrimeQ[x] && PrimeQ[x - 1710], i++]]

I find 90 such prime values. You can replace the i++ with Print[x, " ", x - 1710, " " , 53] to get the pairs yourself.
I'll leave it to you to generalize this to other z values, or to translate this to a coding language that your machine can handle.

Alberico Lepore · 2020-02-24, 00:16

Quote:

Originally Posted by enzocreti

Every integer can be written as x-y+z with x y z primes?

If x, y and z are odd prime numbers

x+z = goldbach

any y

2020-02-23, 22:17	#1
enzocreti Mar 2018 17·31 Posts	Problem... 1763=5879-4423+307 1763 can be written as x-y+z Where x y z are primes Are there other primes x y z such that 1763=x-y+z? Every integer can be written as x-y+z with x y z primes? Are there others primes x y z such that 1763=x-y+z? Last fiddled with by enzocreti on 2020-02-23 at 22:21

2020-02-23, 23:47	#2
Dylan14 "Dylan" Mar 2017 7×79 Posts	An easy way we could do this would be to fix one of the values of x, y and z to a particular prime. For example, let's take z = 53, which is prime. Then your equation becomes 1763 = x - y + 53, or 1710 = x - y which implies y = x - 1710. So we merely need to seek solutions where x and x - 1710 are prime. Using the following Mathematica code Code: For[x = 1711, x <= 3000, x++, If[PrimeQ[x] && PrimeQ[x - 1710], i++]] I find 90 such prime values. You can replace the i++ with Print[x, " ", x - 1710, " " , 53] to get the pairs yourself. I'll leave it to you to generalize this to other z values, or to translate this to a coding language that your machine can handle. Last fiddled with by Dylan14 on 2020-02-23 at 23:48

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