mersenneforum.org Problem...
 Register FAQ Search Today's Posts Mark Forums Read

 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
2020-02-24, 00:16   #3
Alberico Lepore

May 2017
ITALY

52·19 Posts

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

Last fiddled with by Alberico Lepore on 2020-02-24 at 00:31

 Similar Threads Thread Thread Starter Forum Replies Last Post dabler Miscellaneous Math 1 2018-07-28 14:03 MattcAnderson Puzzles 4 2014-08-21 04:40 science_man_88 Software 1 2011-01-31 21:40 derekg Lone Mersenne Hunters 2 2007-02-26 22:47 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

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.