Jonathan P. Sorenson

activity

20152026

most citedA Perspective on Future Research Directions in Information Theory

4 citations · 5 across the 7 of their papers we have counts for

collaborators

8 papers

math.NT2026

Primes and almost primes between cubes

Daniel R. Johnston, Jonathan P. Sorenson, Simon N. Thomas +1

In this paper we study the problem of detecting prime numbers between all consecutive cubes. Firstly, we use a large computation to show that there is always a prime between $n^{3}$ …

math.NT2025

Analysis of Algorithms for Moser's Problems on Sums of Consecutive Primes

Jonathan P. Sorenson, Eleanor Waiss

In his 1963 paper on the sum of consecutive primes, Moser posed four open questions related to $f (n)$ , the number of ways an integer $n$ can be written as a sum of consecutive prim…

math.NT2025

Explicit Bounds and Parallel Algorithms for Counting Multiply Gleeful Numbers

Sara Moore, Jonathan P. Sorenson

Let $k \geq 1$ be an integer. A positive integer $n$ is $k$ -\textit{gleeful} if $n$ can be represented as the sum of $k$ th powers of consecutive primes. For example, $35 = 2^{3} + 3^{3}$ is…

cs.DS2024

Reducing the Space Used by the Sieve of Eratosthenes When Factoring

Samuel Hartman, Jonathan P. Sorenson

We present a version of the sieve of Eratosthenes that can factor all integers $\leq x$ in $O (x lo g lo g x)$ arithmetic operations using at most $O (x / lo g lo g x)$ bits of spa…

math.NT2022

An Algorithm for Ennola's Second Theorem and Counting Smooth Numbers in Practice

Chloe Makdad, Jonathan P. Sorenson

Let $Ψ (x, y)$ count the number of positive integers $n \leq x$ such that every prime divisor of $n$ is at most $y$ . Given inputs $x$ and $y$ , what is the best way to estimate $Ψ (x, y)$ …

math.NT2022★ 1 cited

Computation of the least primitive root

Kevin J. McGown, Jonathan P. Sorenson

Let $g (p)$ denote the least primitive root modulo $p$ , and $h (p)$ the least primitive root modulo $p^{2}$ . We computed $g (p)$ and $h (p)$ for all primes $p \leq 1 0^{16}$ . Here we presen…

math.NT2022

An Algorithm to Find Sums of Powers of Consecutive Primes

Cathal O'Sullivan, Jonathan P. Sorenson, Aryn Stahl

We present and analyze an algorithm to enumerate all integers $n \leq x$ that can be written as the sum of consecutive $k$ th powers of primes, for $k > 1$ . We show that the number of s…

cs.IT2015★ 4 cited

A Perspective on Future Research Directions in Information Theory

Jeffrey G. Andrews, Alexandros Dimakis, Lara Dolecek +15

Information theory is rapidly approaching its 70th birthday. What are promising future directions for research in information theory? Where will information theory be having the mo…