#### Vol. 8, No. 2, 2015

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On the least prime congruent to 1 modulo $n$

### Jackson S. Morrow

Vol. 8 (2015), No. 2, 357–359
##### Abstract

For any integer $n>1$, there are infinitely many primes congruent to $1\phantom{\rule{0.3em}{0ex}}\left(mod\phantom{\rule{0.3em}{0ex}}n\right)$. In this note, the elementary argument of Thangadurai and Vatwani is modified to improve their upper estimate of the least such prime when $n$ itself is a prime greater than or equal to 5.

##### Keywords
primes in progressions, arithmetic progressions
##### Mathematical Subject Classification 2010
Primary: 11B25, 11N13