J. Sorenson

activity

20092020

most citedStrong Pseudoprimes to Twelve Prime Bases

16 citations · 43 across the 10 of their papers we have counts for

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math.NT2020

Algorithms to Uniformly Generate Random Factored Smooth Integers

Eric Bach, Jonathan Sorenson

Let $x \geq y > 0$ be integers. A positive integer is $y$ -smooth if all its prime divisors are at most $y$ . Let $Ψ (x, y)$ count the number of $y$ -smooth integers up to $x$ . We present s…

math.NT2019

An Algorithm and Estimates for the Erdős-Selfridge Function (work in progress)

Brianna Sorenson, Jonathan P Sorenson, Jonathan Webster

Let $p (n)$ denote the smallest prime divisor of the integer $n$ . Define the function $g (k)$ to be the smallest integer $> k + 1$ such that $p ((k g ( k ))) > k$ . So we have $g (2) = 6$ …

math.NT2018★ 4 cited

Two Algorithms to Find Primes in Patterns

Jonathan P. Sorenson, Jonathan Webster

Let $k \geq 1$ be an integer, and let $P = (f_{1} (x), \dots, f_{k} (x))$ be $k$ admissible linear polynomials over the integers, or \textit{the pattern}. We present two algorithms that f…

math.NT2015★ 16 cited

Strong Pseudoprimes to Twelve Prime Bases

Jonathan P. Sorenson, Jonathan Webster

Let $ψ_{m}$ be the smallest strong pseudoprime to the first $m$ prime bases. This value is known for $1 \leq m \leq 11$ . We extend this by finding $ψ_{12}$ and $ψ_{13}$ . We also pres…

math.NT2010★ 4 cited

Sieving for pseudosquares and pseudocubes in parallel using doubly-focused enumeration and wheel datastructures

Jonathan P. Sorenson

We extend the known tables of pseudosquares and pseudocubes, discuss the implications of these new data on the conjectured distribution of pseudosquares and pseudocubes, and presen…