A heuristic asymptotic formula concerning the distribution of prime numbers
HTML articles powered by AMS MathViewer
- by Paul T. Bateman and Roger A. Horn PDF
- Math. Comp. 16 (1962), 363-367 Request permission
References
- Atle Selberg, On an elementary method in the theory of primes, Norske Vid. Selsk. Forh., Trondhjem 19 (1947), no. 18, 64–67. MR 0022871
- Paul T. Bateman and Rosemarie M. Stemmler, Waring’s problem for algebraic number fields and primes of the form $(p^{r}-1)/(p^{d}-1)$, Illinois J. Math. 6 (1962), 142–156. MR 138616
- G. H. Hardy and J. E. Littlewood, Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes, Acta Math. 44 (1923), no. 1, 1–70. MR 1555183, DOI 10.1007/BF02403921 D. H. Lehmer, “Tables concerning the distribution of primes up to 37 millions,” 1957, deposited in the UMT file and reviewed in MTAC v. 13, 1959, p. 56-57. A. E. Western, “Note on the number of primes of the form ${n^2} + 1$,” Proc. Cambridge Philos. Soc., v. 21, 1922, p. 108-109.
- Daniel Shanks, On the conjecture of Hardy & Littlewood concerning the number of primes of the form $n^{2}+a$, Math. Comp. 14 (1960), 320–332. MR 120203, DOI 10.1090/S0025-5718-1960-0120203-6
- Daniel Shanks, A note on Gaussian twin primes, Math. Comput. 14 (1960), 201–203. MR 0111724, DOI 10.1090/S0025-5718-1960-0111724-0
- Daniel Shanks, On numbers of the form $n^{4}+1$, Math. Comput. 15 (1961), 186–189. MR 0120184, DOI 10.1090/S0025-5718-1961-0120184-6 A. Schinzel & W. Sierpiński, “Sur certaines hypothèses concernant les nombres premiers,” Acta Arith., v. 4, 1958, p. 185-208.
- A. Schinzel, Remarks on the paper “Sur certaines hypothèses concernant les nombres premiers”, Acta Arith. 7 (1961/62), 1–8. MR 130203, DOI 10.4064/aa-7-1-1-8
Additional Information
- © Copyright 1962 American Mathematical Society
- Journal: Math. Comp. 16 (1962), 363-367
- MSC: Primary 10.42
- DOI: https://doi.org/10.1090/S0025-5718-1962-0148632-7
- MathSciNet review: 0148632