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 May 20th, 2014, 06:58 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 07:06 PM.
 May 21st, 2014, 03:33 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 $i + j + 2ij , \ i,j\in\mathbb{N},\ 1 \le i \le j$.
 May 21st, 2014, 06:07 AM #3 Global Moderator     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.
May 21st, 2014, 10:22 PM   #4
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Quote:
 Originally Posted by CRGreathouse Right, that's Goldbach's (binary) conjecture.
Thanks! Neil published this, see comments on OEIS A005097.

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