Sierpinski's Prime Sequence Theorem

For any $M$, there exists a $t'$ such that the sequence

$$n^2+t',$$

where $n=1$, 2, ...contains at least $M$ Primes.

See also Dirichlet's Theorem, Fermat 4n+1 Theorem, Sierpinski's Composite Number Theorem

References

Abel, U. and Siebert, H. ``Sequences with Large Numbers of Prime Values.'' Amer. Math. Monthly 100, 167-169, 1993.

Ageev, A. A. ``Sierpinski's Theorem is Deducible from Euler and Dirichlet.'' Amer. Math. Monthly 101, 659-660, 1994.

Forman, R. ``Sequences with Many Primes.'' Amer. Math. Monthly 99, 548-557, 1992.

Garrison, B. ``Polynomials with Large Numbers of Prime Values.'' Amer. Math. Monthly 97, 316-317, 1990.

Sierpinski, W. ``Les binômes $x^2+n$ et les nombres premiers.'' Bull. Soc. Roy. Sci. Liege 33, 259-260, 1964.