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Sierpiński'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's 4n+1 Theorem, Sierpiński's Composite Number Theorem

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

Referenced on Wolfram|Alpha

Sierpiński's Prime Sequence Theorem

Cite this as:

Weisstein, Eric W. "Sierpiński's Prime Sequence Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SierpinskisPrimeSequenceTheorem.html

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