A note on Gaussian twin primes
Author:
Daniel Shanks
Journal:
Math. Comp. 14 (1960), 201203
MSC:
Primary 10.00
MathSciNet review:
0111724
Fulltext PDF Free Access
References 
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Additional Information
 [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/S00255718195901057842
 [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 ,'' Notices, Amer. Math. Soc., v. 6, 1959, p. 417. Abstract 55952. A forthcoming paper with the same title will give an expanded version of this report.
 [4]
J. W. L. Glaisher, ``An enumeration of primepairs,'' Messenger Math., v. 8, 1878. p. 2833.
 [5]
The empirical evidence for (1) is much more extensive. D. H. Lehmer has computed = 183728, = 183582, and = 1.0008 for . 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.
 [1]
 Daniel Shanks, ``A sieve method for factoring numbers of the form .'' MTAC, v. 13, 1959, p. 7886. MR 0105784 (21:4520)
 [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 ,'' Notices, Amer. Math. Soc., v. 6, 1959, p. 417. Abstract 55952. A forthcoming paper with the same title will give an expanded version of this report.
 [4]
 J. W. L. Glaisher, ``An enumeration of primepairs,'' Messenger Math., v. 8, 1878. p. 2833.
 [5]
 The empirical evidence for (1) is much more extensive. D. H. Lehmer has computed = 183728, = 183582, and = 1.0008 for . 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/S00255718196001117240
PII:
S 00255718(1960)01117240
Article copyright:
© Copyright 1960
American Mathematical Society
