Related papers: Computing an Integer Prime Factoring in O(n^2.5)

We analyze algorithms for computing the $n$th prime $p_n$ and establish asymptotic bounds for several approaches. Using existing results on the complexity of evaluating the prime-counting function $\pi(x)$, we show that the binary search…

This paper has been withdrawn by the author, due to a crucial error in the proof of Lemma 3.1.

This paper had been withdrawn because the prime reported effect had not been confirmed in further investigations (see arXiv:0812.4488 [hep-lat]).

Integer multiplication has long been considered a hard problem for neural networks, with the difficulty widely attributed to the O(n) long-range dependency induced by carry chains. We argue that this diagnosis is wrong: long-range…

This paper has been withdrawn by the author due to a crucial error.

We assume the permutation $\pi$ is given by an $n$-element array in which the $i$-th element denotes the value $\pi(i)$. Constructing its inverse in-place (i.e. using $O(\log{n})$ bits of additional memory) can be achieved in linear time…

We prove that the complexity of computing the table of primes between $1$ and $n$ on a multitape Turing machine is $O(n \log n)$.

The paper is withdrawn.

Probabilistic computing has been introduced to operate functional networks using a probabilistic bit (p-bit), generating 0 or 1 probabilistically from its electrical input. In contrast to quantum computers, probabilistic computing enables…

The paper has been withdrawn due to an error in Lemma 1.

Let $b \ge 2$ be an integer. Not much is known on the representation in base $b$ of prime numbers or of numbers whose prime factors belong to a given, finite set. Among other results, we establish that any sufficiently large integer which…

Withdrawn because of non-correctness. Would have implied too much to be true :-|

This paper has been withdrawn due to errors in the analysis of data with Carrier Access Rate control and statistical methodologies.

This article has been withdrawn due to an error in a proof of the main result.

This article is withdrawn because of a mistake in the main result of the paper.

Assuming a conjectural upper bound for the least prime in an arithmetic progression, we show that n-bit integers may be multiplied in O(n log n 4^(log^* n)) bit operations.

We give an endorsement for Cornacchia's famous algorithm. Thus we do not claim anything new but an approach which is supposed to be simpler than those of previous works written with the same aim.

Numerical data processing is a key task across different fields of computer technology use. However, even simple summation of values is not precise due to the floating point representation use. This paper presents a practical algorithm for…

The paging problem is that of deciding which pages to keep in a memory of k pages in order to minimize the number of page faults. This paper introduces the marking algorithm, a simple randomized on-line algorithm for the paging problem, and…

This paper has been withdrawn as we discovered a bug in our tensorflow implementation that involved accidental mixing of vectors across batches. This lead to different inference results given different batch sizes which is completely…