Go Back > Extra Stuff > Blogorrhea > enzocreti

Thread Tools
Old 2020-02-23, 22:17   #1
Mar 2018

17·31 Posts
Default Problem...


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

Are there other primes x y z such that


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

Are there others primes x y z such that

Last fiddled with by enzocreti on 2020-02-23 at 22:21
enzocreti is offline   Reply With Quote
Old 2020-02-23, 23:47   #2
Dylan14's Avatar
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

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
Dylan14 is online now   Reply With Quote
Old 2020-02-24, 00:16   #3
Alberico Lepore
Alberico Lepore's Avatar
May 2017

52·19 Posts

Originally Posted by enzocreti View Post

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

Last fiddled with by Alberico Lepore on 2020-02-24 at 00:31
Alberico Lepore is offline   Reply With Quote

Thread Tools

Similar Threads
Thread Thread Starter Forum Replies Last Post
A new problem similar to the Collatz problem dabler Miscellaneous Math 1 2018-07-28 14:03
problem 2.4 MattcAnderson Puzzles 4 2014-08-21 04:40
problem with my PC science_man_88 Software 1 2011-01-31 21:40
Problem with LMH derekg Lone Mersenne Hunters 2 2007-02-26 22:47
51 problem Neves Puzzles 15 2004-02-05 23:11

All times are UTC. The time now is 15:25.

Sat Jan 23 15:25:55 UTC 2021 up 51 days, 11:37, 0 users, load averages: 2.04, 1.90, 1.96

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.