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Let $X$ be the set of natural numbers $k_i$, $k_i \geq 1$, with the property that at least one of the equations $p_i = $6$ k_i \pm 1$ gives the $i$-th prime number (disregarding $2$ and $3$), and define the set $Y$ to be $Y = \mathbb{N} \setminus \{1\}$. Is it true that each element of Y can be represented as $2 k_i$ or as the sum $k_i + k_j$, where $k_i$ and $k_j$ are both elements of set X?

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    [Crossposted to MO](http://mathoverflow.net/questions/74973/)2011-09-09
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    X is also infinite since there is infinite number of primes2011-09-09
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    anon,minimal element of X is k=1 so 2 can be represented as 2*12011-09-09
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    Dan,it states..."Let X be a set of natural numbers k_i....with the property..."2011-09-09
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    I've edited the question to clarify the meaning pedja had in mind. @Dan2011-09-09
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    Dan,I think that i was precise enough but I will accept any profound criticism of formulation2011-09-09
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    anon,you are right..this is better formulation2011-09-09

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