## Lal's Constant

Let denote the number of Primes of the form for , then

 (1)

where is the Logarithmic Integral (Shanks 1960, pp. 321-332). Let denote the number of Primes of the form for , then
 (2)

(Shanks 1961, 1962). Let denote the number of pairs of Primes and for , then
 (3)

where
 (4)

(Shanks 1960, pp. 201-203). Finally, let denote the number of pairs of Primes and for , then
 (5)

(Lal 1967), where 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.