# 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} }

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…

## One Citation

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