A note on Gaussian twin primes
Author:
Daniel Shanks
Journal:
Math. Comp. 14 (1960), 201-203
MSC:
Primary 10.00
DOI:
https://doi.org/10.1090/S0025-5718-1960-0111724-0
MathSciNet review:
0111724
Full-text PDF Free Access
References | Similar Articles | Additional Information
- Daniel Shanks, A sieve method for factoring numbers of the form $n^{2}+1$, Math. Tables Aids Comput. 13 (1959), 78–86. MR 105784, DOI https://doi.org/10.1090/S0025-5718-1959-0105784-2 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. 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. J. W. L. Glaisher, “An enumeration of prime-pairs,” Messenger Math., v. 8, 1878. p. 28-33. 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.
Retrieve articles in Mathematics of Computation with MSC: 10.00
Retrieve articles in all journals with MSC: 10.00
Additional Information
Article copyright:
© Copyright 1960
American Mathematical Society