• [1] Daniel Shanks, A sieve method for factoring numbers of the form 𝑛²+1, Math. Tables Aids Comput. 13 (1959), 78–86. MR 105784, https://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 ,'' 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 = 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.

Bibliography

[1]

Daniel Shanks, ``A sieve method for factoring numbers of the form .'' MTAC, v. 13, 1959, p. 78-86. 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 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 = 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.