Bateman, P. T.; Horn, Roger A. A heuristic asymptotic formula concerning the distribution of prime numbers. (English) Zbl 0105.03302 Math. Comput. 16, 363-367 (1962). Reviewer: A. Schinzel (Warszawa) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 ReviewsCited in 91 Documents MSC: 11N05 Distribution of primes Keywords:heuristic asymptotic formula; distribution of prime numbers Citations:JFM 48.0143.04; Zbl 0082.25802 PDF BibTeX XML Cite \textit{P. T. Bateman} and \textit{R. A. Horn}, Math. Comput. 16, 363--367 (1962; Zbl 0105.03302) Full Text: DOI Online Encyclopedia of Integer Sequences: Primes of the form k^2 + 1. Primes p such that p^2 + p + 1 is prime. Numbers n that generate 5 primes under the first 5 iterations of the map n->A002731(n). Decimal expansion of Product_{primes p} (1-1/p)^(-2)*(1-(2+A102283(p))/p). Primes of the form 4n^3 + 1. References: [1] Atle Selberg, On an elementary method in the theory of primes, Norske Vid. Selsk. Forh., Trondhjem 19 (1947), no. 18, 64 – 67. · Zbl 0041.01903 [2] Paul T. Bateman and Rosemarie M. Stemmler, Waring’s problem for algebraic number fields and primes of the form (\?^{\?}-1)/(\?^{\?}-1), Illinois J. Math. 6 (1962), 142 – 156. · Zbl 0107.03903 [3] 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. · JFM 48.0143.04 [4] 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. [5] 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. · JFM 48.1181.01 [6] Daniel Shanks, On the conjecture of Hardy & Littlewood concerning the number of primes of the form \?²+\?, Math. Comp. 14 (1960), 320 – 332. · Zbl 0098.03705 [7] Daniel Shanks, A note on Gaussian twin primes, Math. Comput. 14 (1960), 201 – 203. · Zbl 0099.03102 [8] Daniel Shanks, On numbers of the form \?\(^{4}\)+1, Math. Comput. 15 (1961), 186 – 189. · Zbl 0104.03703 [9] A. Schinzel & W. Sierpiński, “Sur certaines hypothèses concernant les nombres premiers,” Acta Arith., v. 4, 1958, p. 185-208. [10] A. Schinzel, Remarks on the paper ”Sur certaines hypothèses concernant les nombres premiers”, Acta Arith. 7 (1961/1962), 1 – 8. · Zbl 0101.27902 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.