Prime numbers p with expression p=a2±ab±b2

Intervals with few Prime Numbers

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Prime numbers with Beatty sequences

A study of certain Hamiltonian systems has lead Y. Long to conjecture the existence of infinitely many primes of the form p = 2 ⌊αn⌋+1, where 1 < α < 2 is a fixed irrational number. An argument of P. Ribenboim coupled with classical results about the distribution of fractional parts of irrational multiples of primes in an arithmetic progression immediately imply that this conjecture holds in a ...

-bialgebras associated with prime numbers

Let O∗ be the C-algebra defined as the direct sum of all Cuntz algebras. Then O∗ has a non-cocommutative comultiplication ∆φ and a counit ε. Let BI(O∗) denote the set of all closed biideals of the C-bialgebra (O∗,∆φ, ε) and let P(P) denote the power set of the set of all prime numbers. We show a one-to-one correspondence between BI(O∗) and P(P). Furthermore, we show that for any I in BI(O∗), th...

Prime Slaughter: Playful Prime Numbers

Starting from the difficulty of creating playful representation of domain-specific abstract concepts, this study discusses the design of Prime Slaughter, a computer game aimed at facilitating individual sense-making of abstract mathematical concepts. Specifically the game proposes a transpositionmathematical concepts. Specifically the game proposes a transposition of primality and factorization...

Numbers with a large prime factor