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A heuristic asymptotic formula concerning the distribution of prime numbers. (English) Zbl 0105.03302

MSC:
11N05 Distribution of primes
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[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 · doi:10.1007/BF02403921 · doi.org
[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
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