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On the Gaussian primes on the line $ {\rm Im}(X)=1$


Author: M. C. Wunderlich
Journal: Math. Comp. 27 (1973), 399-400
MSC: Primary 65A05; Secondary 10A25
DOI: https://doi.org/10.1090/S0025-5718-1973-0326973-5
MathSciNet review: 0326973
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Abstract: This paper contains a summary table of the author's computation of the Gaussian primes of the form $ a + i$. For the values $ x = 1000, 10000, 100000, 180000$, and 500000 (500000) 14000000, the following values are tabulated: $ G(x)$, the numbers of Gaussisn primes $ a + i$ with $ a \leqq 14000000;{\pi _1}(x)$, the number of primes $ \leqq x$ congruent to $ 1 mod 4$; $ {\pi _3}(x)$, the number of primes $ \leqq x$ congruent to $ 3 mod 4$; and $ G(x)/{\pi _3}(x)$.


References [Enhancements On Off] (What's this?)

  • [1] 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. 48. MR 1555183
  • [2] Daniel Shanks, "A sieve method for factoring numbers of the form $ {n^2} + 1$," MTAC, v. 13, 1959, pp. 78-86. MR 21 #4520. MR 0105784 (21:4520)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1973-0326973-5
Article copyright: © Copyright 1973 American Mathematical Society

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