1,273
Views
0
CrossRef citations to date
0
Altmetric
Notes

A Conjecture on Primes in Arithmetic Progressions and Geometric Intervals

ORCID Icon &
Pages 979-983 | Received 09 Apr 2021, Accepted 09 Feb 2022, Published online: 06 Oct 2022

References

  • Bach, E., Shallit, J. (1996). Algorithmic Number Theory, Vol. 1: Efficient Algorithms. Cambridge, MA: MIT Press.
  • Bennett, A. M., Martin, G., O’Bryant, K., Rechnitzer, A. (2018). Explicit bounds for primes in arithmetic progressions. Illinois J. Math. 62(1–4): 427–532. DOI: 10.1215/ijm/1552442669.
  • Bombieri, E., Friedlander, J. B., Iwaniec, H. (1989). Primes in arithmetic progressions to large moduli. III. J. Amer. Math. Soc. 2(2): 215–224. DOI: 10.1090/S0894-0347-1989-0976723-6.
  • Carmichael, R. D. (1907). On Euler’s ϕ-function. Bull. Amer. Math. Soc. 13(5): 241–243. DOI: 10.1090/S0002-9904-1907-01453-2.
  • Carmichael, R. D. (1922). Note on Euler’s φ-function. Bull. Amer. Math. Soc. 28(3): 109–110. DOI: 10.1090/S0002-9904-1922-03504-5.
  • Chowla, S. (1934). On the least prime in an arithmetical progression. Acta Arith. 1(2): 1–3.
  • Dirichlet, P. G. L. (1837). Beweis des Satzes, dass jede unbegrenzte arithmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Factor sind, unendlich viele Primzahlen enthält. Abh. K. Preuss. Akad. Wiss. 45–81.
  • Ford, K. (1998). The distribution of totients. Ramanujan J. 2(1–2): 67–151. doi.org/ DOI: 10.1023/A:1009761909132.
  • Heath-Brown, D. R. (1992). Zero-free regions for Dirichlet L-functions, and the least prime in an arithmetic progression. Proc. London Math. Soc. 64(2): 265–338. DOI: 10.1112/plms/s3-64.2.265.
  • Linnik, U. V. (1944). On the least prime in an arithmetic progression. I. The basic theorem. Rec. Math. [Mat. Sbornik] N.S. 15(57): 139–178. mi.mathnet.ru/eng/msb6196
  • Linnik, U. V. (1944). On the least prime in an arithmetic progression. II. The Deuring-Heilbronn phenomenon. Rec. Math. [Mat. Sbornik] N.S. 15(57): 347–368. mi.mathnet.ru/eng/msb6202
  • Pomerance, C. (1974). On Carmichael’s conjecture. Proc. Amer. Math. Soc. 43(2): 297–298. DOI: 10.1090/S0002-9939-1974-0340161-0.
  • Schinzel, A., Sierpiński, W. (1958). Sur certaines hypothèses concernant les nombres premiers. Acta Arith. 4(3): 185–208. eudml.org/doc/206115
  • Xylouris, T. (2018). Linniks Konstante ist kleiner als 5.Chebyshevskii Sb. 19(3): 80–94. DOI: 10.22405/2226-8383-2018-19-3-80-94.