Add to ORKGWe introduce a refinement of the GPY sieve method for studying prime kk-tuples and small gaps between primes. This refinement avoids previous limitations of the method and allows us to show that for each kk, the prime kk-tuples conjecture holds for a positive proportion of admissible kk-tuples. In particular, lim infn(pn+m−pn)<∞lim infn(pn+m−pn)<∞ for every integer mm. We also show that lim inf(pn+1−pn)≤600lim inf(pn+1−pn)≤600 and, if we assume the Elliott-Halberstam conjecture, that lim infn(pn+1−pn)≤12lim infn(pn+1−pn)≤12 and lim infn(pn+2−pn)≤600lim infn(pn+2−pn)≤600
. By a prime gap of size g, we mean that there are primes p and p+g such that the g \Gamma 1 numbers...
Abstract. For any m ě 1, let Hm denote the quantity Hm: “ lim infnÑ8ppn`m ´ pnq, where pn denotes th...
Abstract. The classical memoir by Riemann on the zeta function was motivated by questions about the ...
We introduce a refinement of the GPY sieve method for studying prime kk-tuples and small gaps betwee...
We discuss recent advances on weak forms of the Prime k-tuple Conjecture, and its role in proving ne...
The twin prime conjecture - that there exist infinitely many pairs of "twin primes" p, p + 2 - is am...
Abstract. Fix an integer g 6 = −1 that is not a perfect square. In 1927, Artin conjectured that ther...
michaelnielsen.org/polymath1/ index.php?title=Bounded_gaps_ between_primes, Full list of author info...
We introduce a method for showing that there exist prime numbers which are very close together. The ...
Let r ≥ 2 be an integer. We adapt the Maynard–Tao sieve to produce the asymptotically best-known bou...
In this dissertation we consider the problem of finding small prime gaps in various sets $\mathcal{C...
In this dissertation we consider the problem of finding small prime gaps in various sets $\mathcal{C...
Let $p_n$ be the $n$th smallest prime and $d_n\defeq p_{n+1}-p_n$ the gap between $p_n$ and $p_{n+1}...
In this paper proof of the Polignac's Conjecture for gaps bigger than four is going to be presented....
Five conjectures on the gaps between consecutive primes are formulated. One expresses the number of ...
. By a prime gap of size g, we mean that there are primes p and p+g such that the g \Gamma 1 numbers...
Abstract. For any m ě 1, let Hm denote the quantity Hm: “ lim infnÑ8ppn`m ´ pnq, where pn denotes th...
Abstract. The classical memoir by Riemann on the zeta function was motivated by questions about the ...
We introduce a refinement of the GPY sieve method for studying prime kk-tuples and small gaps betwee...
We discuss recent advances on weak forms of the Prime k-tuple Conjecture, and its role in proving ne...
The twin prime conjecture - that there exist infinitely many pairs of "twin primes" p, p + 2 - is am...
Abstract. Fix an integer g 6 = −1 that is not a perfect square. In 1927, Artin conjectured that ther...
michaelnielsen.org/polymath1/ index.php?title=Bounded_gaps_ between_primes, Full list of author info...
We introduce a method for showing that there exist prime numbers which are very close together. The ...
Let r ≥ 2 be an integer. We adapt the Maynard–Tao sieve to produce the asymptotically best-known bou...
In this dissertation we consider the problem of finding small prime gaps in various sets $\mathcal{C...
In this dissertation we consider the problem of finding small prime gaps in various sets $\mathcal{C...
Let $p_n$ be the $n$th smallest prime and $d_n\defeq p_{n+1}-p_n$ the gap between $p_n$ and $p_{n+1}...
In this paper proof of the Polignac's Conjecture for gaps bigger than four is going to be presented....
Five conjectures on the gaps between consecutive primes are formulated. One expresses the number of ...
. By a prime gap of size g, we mean that there are primes p and p+g such that the g \Gamma 1 numbers...
Abstract. For any m ě 1, let Hm denote the quantity Hm: “ lim infnÑ8ppn`m ´ pnq, where pn denotes th...
Abstract. The classical memoir by Riemann on the zeta function was motivated by questions about the ...