A heuristic asymptotic formula concerning the distribution of prime numbers

Authors:
Paul T. Bateman and Roger A. Horn

Journal:
Math. Comp. **16** (1962), 363-367

MSC:
Primary 10.42

DOI:
https://doi.org/10.1090/S0025-5718-1962-0148632-7

Remarks:
Math. Comp. **17**, no. 84 (1963), pp. 445-447.

MathSciNet review:
0148632

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References | Similar Articles | Additional Information

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*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 https://doi.org/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 - 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 https://doi.org/10.1090/S0025-5718-1960-0120203-6 - Daniel Shanks,
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A. Schinzel & W. Sierpiński, “Sur certaines hypothèses concernant les nombres premiers,” - A. Schinzel,
*Remarks on the paper “Sur certaines hypothèses concernant les nombres premiers”*, Acta Arith.**7**(1961/62), 1–8. MR**130203**, DOI https://doi.org/10.4064/aa-7-1-1-8

*MTAC*v. 13, 1959, p. 56-57. A. E. Western, “Note on the number of primes of the form ${n^2} + 1$,”

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Article copyright:
© Copyright 1962
American Mathematical Society