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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

A note on Gaussian twin primes


Author: Daniel Shanks
Journal: Math. Comp. 14 (1960), 201-203
MSC: Primary 10.00
MathSciNet review: 0111724
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  • [1] Daniel Shanks, A sieve method for factoring numbers of the form 𝑛²+1, Math. Tables Aids Comput. 13 (1959), 78–86. MR 0105784 (21 #4520), http://dx.doi.org/10.1090/S0025-5718-1959-0105784-2
  • [2] G. H. Hardy & J. E. Littlewood, ``Partitio numerorum III: On the expression of a number as a sum of primes,'' Acta. Math., v. 44, 1923, p. 42.
  • [3] Daniel Shanks, ``On the conjecture of Hardy and Littlewood concerning the number of primes of the form $ {n^2} + a$,'' Notices, Amer. Math. Soc., v. 6, 1959, p. 417. Abstract 559-52. A forthcoming paper with the same title will give an expanded version of this report.
  • [4] J. W. L. Glaisher, ``An enumeration of prime-pairs,'' Messenger Math., v. 8, 1878. p. 28-33.
  • [5] The empirical evidence for (1) is much more extensive. D. H. Lehmer has computed $ z(N)$ = 183728, $ \overline z (N)$ = 183582, and $ {z}/{z}(N)$ = 1.0008 for $ N = {37.10^6}$. See the review, UMT 3, of D. H. Lehmer, ``Tables concerning the distribution of primes up to 37 million,'' MTAC, v. 13, 1959, p. 56.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1960-0111724-0
PII: S 0025-5718(1960)0111724-0
Article copyright: © Copyright 1960 American Mathematical Society