A note on Gaussian twin primes

Author:
Daniel Shanks

Journal:
Math. Comp. **14** (1960), 201-203

MSC:
Primary 10.00

MathSciNet review:
0111724

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**[1]**Daniel Shanks,*A sieve method for factoring numbers of the form 𝑛²+1*, Math. Tables Aids Comput.**13**(1959), 78–86. MR**0105784**, 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.

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DOI:
https://doi.org/10.1090/S0025-5718-1960-0111724-0

Article copyright:
© Copyright 1960
American Mathematical Society