6
votes
1answer
481 views

Is this weak asymptotic Goldbach's conjecture open?

Let $\tau(x)$ be the number of even numbers $2<2n<x$ which can't be written as a sum of two primes. Goldbach's conjecture: $\tau(x) = 0$ Asymptotic Goldbach's conjecture: $\tau(x) = O(1) $ ...
0
votes
0answers
191 views

Relationship between this conjecture and Lehmer's Theorem?

Let A be: n such that $\ \frac{n-1}{ord_n 2}=2^x\ $ and $n$ with the conditions of the conjecture in OEIS A226014,$\ n \in \mathbb{Z^+} ,\ x \in \mathbb{Z}_{\geq 0},\ $then $n$ is prime ...
6
votes
0answers
193 views

Does the Maynard-Tao Theorem apply to general tuples of linear forms?

In the paper http://arxiv.org/pdf/1311.5319v1.pdf the author states the following theorem, which he attributes to Maynard and Tao. For any integer $m > 2$, there exists an integer $k = k(m)$ such ...
7
votes
1answer
309 views

Are primes of density 0 in $a\cdot b^n+c$?

Hooley proves in Applications of Sieves to the Theory of Numbers that there are only $o(x)$ numbers $n\le x$ such that $n\cdot2^n+1$ is a (Cullen) prime. The proof generalizes to forms ...
4
votes
0answers
80 views

On a weighted sum in a lemma for sieve methods

I'm reading James Maynard's paper "Small gaps between primes". Lemma 6.1 (p.14) in this paper confused me. This lemma was taken from Goldston-Graham-Pintz-Yildirim's paper "Small gaps between ...
8
votes
0answers
333 views

Sieve bound for prime $k$-tuples

Let $d_1<d_2<\dots<d_k$ be integers. Then the number of integers $n\leq x$, such that $n+d_1, n+d_2, \ldots, n+d_k$ are simultaneously prime, is bounded above by $$ \mathfrak{S}(d_1, \ldots, ...
2
votes
0answers
141 views

Best known Upper bound on Twin Primes [duplicate]

I know that there is a result from J Wu that the number of twin primes less than a given magnitude $N$ does not exceed $$\frac{2aCN}{\log^2{N}}$$ Where $C=\prod \frac{p(p-2)}{(p-1)^2}$ and $a$ is ...
5
votes
1answer
224 views

Large gaps between P2s

Gaps between consecutive primes are $O(n^{\theta+\varepsilon})$ for $\theta=0.525$ and any $\varepsilon>0.$ I was wondering if a better result is known for gaps between numbers with at most two ...
19
votes
3answers
724 views

Are sets with similar asymptotic behavior as the primes necessarily finite additive bases?

The set of primes $\mathbb{P}$ has many interesting properties in additive number theory and some of the most famous open problems about $\mathbb{P}$ are the well-known Goldbach's strong and weak ...
2
votes
1answer
237 views

10 factors for x^2 coefficient in quadratic sieve?

I wrote a quadratic sieve and I tried plugging in all the same parameters as the wikipedia article says msieve uses: http://en.wikipedia.org/wiki/Quadratic_sieve#Parameters_from_realistic_example It ...