Linnik's Constant

The constant $L$ in Linnik's Theorem. Heath-Brown (1992) has shown that $L\leq 5.5$, and Schinzel, Sierpinski, and Kanold (Ribenboim 1989) have conjectured that $L=2$.

References

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/linnik/linnik.html

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 13, 1994.

Heath-Brown, D. R. ``Zero-Free Regions for Dirichlet $L$-Functions and the Least Prime in an Arithmetic Progression.'' Proc. London Math. Soc. 64, 265-338, 1992.

Ribenboim, P. The Book of Prime Number Records, 2nd ed. New York: Springer-Verlag, 1989.