On the least prime congruent to 1 modulo $n$

Jackson Morrow

doi:10.2140/involve.2015.8.357

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Home > Journals > Involve > Volume 8 > Issue 2 > Article

2015 On the least prime congruent to 1 modulo $n$

Jackson Morrow

Involve 8(2): 357-359 (2015). DOI: 10.2140/involve.2015.8.357

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Abstract

For any integer $n > 1$ , there are infinitely many primes congruent to $1 (mod n)$ . 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.