# Two Algorithms to Find Primes in Patterns

@article{Sorenson2020TwoAT,
title={Two Algorithms to Find Primes in Patterns},
author={J. Sorenson and Jonathan Webster},
journal={Math. Comput.},
year={2020},
volume={89},
pages={1953-1968}
}
• Published 23 July 2018
• Mathematics, Computer Science
• Math. Comput.
Let $k\ge 1$ be an integer, and let $P= (f_1(x), \ldots, f_k(x) )$ be $k$ admissible linear polynomials over the integers, or \textit{the pattern}. We present two algorithms that find all integers $x$ where $\max{ \{f_i(x) \} } \le n$ and all the $f_i(x)$ are prime. Our first algorithm takes at most $O_P(n/(\log\log n)^k)$ arithmetic operations using $O(k\sqrt{n})$ space. Our second algorithm takes slightly more time, $O_P(n/(\log \log n)^{k-1})$ arithmetic operations, but uses only $n^{1/c… 1 Citations An Algorithm and Estimates for the Erdős-Selfridge Function (work in progress) • Mathematics Open Book Series • 2020 A new algorithm to compute the value of g(k) is presented, and computational evidence is provided to support the claim that$\hat{g}(K)$estimates reasonably well in practice, and it is proved that for large$x, $G(x,k)$ is asymptotic to $x/\hat{ g)$.

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