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

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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), 78â€“86. MR**105784**, DOI https://doi.org/10.1090/S0025-5718-1959-0105784-2
G. H. Hardy & J. E. Littlewood, â€śPartitio numerorum III: On the expression of a number as a sum of primes,â€ť

*Acta. Math.*, v. 44, 1923, p. 42. Daniel Shanks, â€śOn the conjecture of Hardy and Littlewood concerning the number of primes of the form ${n^2} + a$,â€ť

*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, â€śAn enumeration of prime-pairs,â€ť

*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, â€śTables concerning the distribution of primes up to 37 million,â€ť

*MTAC*, v. 13, 1959, p. 56.

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Article copyright:
© Copyright 1960
American Mathematical Society