Results for 'Sławomir Wacewicz'

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  1. The Physical Impossibility of Machine Computations on Sufficiently Large Integers Inspires an Open Problem That Concerns Abstract Computable Sets X⊆N and Cannot Be Formalized in ZFC as It Refers to Our Current Knowledge on X.Apoloniusz Tyszka & Sławomir Kurpaska - manuscript
    Edmund Landau's conjecture states that the set P(n^2+1) of primes of the form n^2+1 is infinite. Let β=(((24!)!)!)!, and let Φ denote the implication: card(P(n^2+1))<ω ⇒ P(n^2+1)⊆(-∞,β]. We heuristically justify the statement Φ without invoking Landau's conjecture. Open problem: Is there a set X⊆N that satisfies conditions (1)--(5)? (1) There are a large number of elements of X and it is conjectured that X is infinite. (2) No known algorithm decides the finiteness/infiniteness of X . (3) There is a known (...)
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