My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum


Reply
 
LinkBack Thread Tools Display Modes
May 20th, 2014, 07:58 PM   #1
Member
 
Joined: Oct 2010

Posts: 72
Thanks: 3

This conjecture is equivalent to the Goldbach's conjecture

I conjecture : every integer greater than 1 can be a plus b, while both 2a + 1 and 2b + 1 are primes. i.e.: 2 = 1 + 1, both 2 * 1 + 1 = 3 are primes.
Or: the set of the sum of every two elements of {n | 2n+1∈P} is the set of integers greater than 1. i.e.:1+1=2, 1+2=3, ..., 5+5=10,....

This is equivalent to the Goldbach's conjecture: every even integers greater than or equal to 6 can be expressed as the sum of two odd primes.

Any revise in my conjecture?

Last edited by miket; May 20th, 2014 at 08:06 PM.
miket is offline  
 
May 21st, 2014, 04:33 AM   #2
Member
 
Joined: Oct 2010

Posts: 72
Thanks: 3

Or: for every integer $n$ greater than $1$, from $1$ to $n - 1$ ,there's a integer k that both $k$ and $n - k$ are not of the form $i + j + 2ij , \ i,j\in\mathbb{N},\ 1 \le i \le j$.
miket is offline  
May 21st, 2014, 07:07 AM   #3
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 937

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Right, that's Goldbach's (binary) conjecture.
CRGreathouse is offline  
May 21st, 2014, 11:22 PM   #4
Member
 
Joined: Oct 2010

Posts: 72
Thanks: 3

Quote:
Originally Posted by CRGreathouse View Post
Right, that's Goldbach's (binary) conjecture.
Thanks! Neil published this, see comments on OEIS A005097.
miket is offline  
Reply

  My Math Forum > College Math Forum > Number Theory

Tags
conjecture, equivalent, goldbach



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Goldbach-like Conjecture mathbalarka Number Theory 3 July 2nd, 2013 10:01 AM
Goldbach's conjecture ibougueye Number Theory 1 August 13th, 2012 09:28 PM
Goldbach Conjecture julian21 Number Theory 1 September 29th, 2010 12:26 AM
Enchev's conjecture - Goldbach's conjecture for twin pairs enchev_eg Number Theory 30 September 28th, 2010 09:43 PM
Goldbach conjecture brunojo Number Theory 109 June 17th, 2009 08:08 PM





Copyright © 2017 My Math Forum. All rights reserved.