A note on the least prime in an arithmetic progression

DOI10.1016/0022-314X(80)90056-6zbMath0436.10020MaRDI QIDQ1140676

Carl B. Pomerance

Publication date: 1980

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

lower boundsJacobsthal functionleast prime in an arithmetic progression

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Primes in congruence classes (11N13) Sieves (11N35)

Related Items (20)

On the gaps between consecutive primes ⋮ On admissible constellations of consecutive primes ⋮ Domination and upper domination of direct product graphs ⋮ Greatest of the Least Primes in Arithmetic Progressions Having a Given Modulus ⋮ Progress towards a nonintegrality conjecture ⋮ On a problem of Recaman and its generalization ⋮ On primes in arithmetic progressions ⋮ Long gaps between primes ⋮ Proof of the \(P\)-integer conjecture of Pomerance ⋮ An explicit upper bound for the least prime ideal in the Chebotarev density theorem ⋮ On generalizations of problems of Recaman and Pomerance ⋮ A FAMILY OF ASYMPTOTICALLY GOOD LATTICES HAVING A LATTICE IN EACH DIMENSION ⋮ A note on large gaps between consecutive primes in arithmetic progressions ⋮ Prime values of polynomials and irreducibility testing ⋮ An upper bound on Jacobsthal’s function ⋮ ON THE MINIMUM ABSOLUTE VALUE OF THE DISCRIMINANT OF ABELIAN FIELDS OF DEGREE p² ⋮ Updating the error term in the prime number theorem ⋮ Disproof of a conjecture of Jacobsthal ⋮ The Möbius function and statistical mechanics ⋮ On the regularity of primes in arithmetic progressions

Cites Work

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• Sur certaines hypothèses concernant les nombres premiers
• Über die kleinste Primzahl einer arithmetischen Reihe.
• The least prime in an arithmetic progression with prime difference.
• ON THE PROBLEM OF JACOBSTHAL
• Greatest of the Least Primes in Arithmetic Progressions Having a Given Modulus
• Primes in intervals
• Remark on the paper of K. Prachar „Über die kleinste Primzahl einer arithmetischen Reihe“.
• On the Integers Relatively Prime to $n$ and a Number-Theoretic Function Considered by Jacobsthal.
• The Difference between Consecutive Prime Numbers V
• On the difference of consecutive numbers prime to n

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