| 释义 |
Lal's ConstantLet  denote the number of Primes of the form  for  , then
 | (1) |
 is the Logarithmic Integral (Shanks 1960, pp. 321-332). Let  denote the number of Primes ofthe form  for , then
 | (2) |
 denote the number of pairs of Primes  and  for  , then
 | (3) |
 | (4) |
 denote the number of pairs of Primes  and  for , then
 | (5) |
 is called Lal's constant. Shanks (1967) showed that  .
References
Lal, M. ``Primes of the Form .'' Math. Comput. 21, 245-247, 1967.Shanks, D. ``On the Conjecture of Hardy and Littlewood Concerning the Number of Primes of the Form  .'' Math. Comput. 14, 321-332, 1960. Shanks, D. ``On Numbers of the Form .'' Math. Comput. 15, 186-189, 1961. Shanks, D. Corrigendum to ``On the Conjecture of Hardy and Littlewood Concerning the Number of Primes of the Form .'' Math. Comput. 16, 513, 1962. Shanks, D. ``Lal's Constant and Generalization.'' Math. Comput. 21, 705-707, 1967.
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