Abstract
The well-known twin prime conjecture states that there are infinitely many primes p such that p + 2 is also a prime. Although the proof of this seemingly simple statement is hopeless at present many further connected conjectures exist. The conjecture in the title, for example, asks if k linear polynomials with suitable conditions on the coefficients represent simultaneously primes infinitely often. One can even ask how ofen this happens. In 1962 Bateman and Horn [2] gave a corresponding quantative conjectures with heuristic evidence. Before stating this conjecture we need to introduce some notations and conventions.
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References
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Dedicated to Professor Paul Bateman on the occasion of his 70th birthday
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© 1990 Bikhäuser Boston
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Balog, A. (1990). The Prime k-Tuplets Conjecture on Average. In: Berndt, B.C., Diamond, H.G., Halberstam, H., Hildebrand, A. (eds) Analytic Number Theory. Progress in Mathematics, vol 85. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3464-7_5
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DOI: https://doi.org/10.1007/978-1-4612-3464-7_5
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