Inclusive prime number races
نویسندگان
چکیده
منابع مشابه
Prime Number Races
There’s nothing quite like a day at the races . . . . The quickening of the pulse as the starter’s pistol sounds, the thrill when your favorite contestant speeds out into the lead (or the distress if another contestant dashes out ahead of yours), and the accompanying fear (or hope) that the leader might change. And what if the race is a marathon? Maybe one of the contestants will be far stronge...
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This Research in Teams meeting focused on the finer behaviour of the function π(x; q, a), which denotes the number of prime numbers of the form qn+ a that are less than or equal to x. Dirichlet’s famous theorem on primes in arithmetic progressions asserts that that there are infinitely many primes of the form qn + a when a is a reduced residue modulo q (that is, when a and q are relatively prim...
متن کاملOptimus prime: paraphrasing prime number talk
Baker (Mind 114:223–238, 2005; Brit J Philos Sci 60:611–633, 2009) has recently defended what he calls the “enhanced” version of the indispensability argument for mathematical Platonism. In this paper I demonstrate that the nominalist can respond to Baker’s argument. First, I outline Baker’s argument in more detail before providing a nominalistically acceptable paraphrase of prime-number talk. ...
متن کاملThe Prime Number Graph
Let pn denote the nth prime. The prime number graph is the set of lattice points (n, pn), n = 1, 2.We show that for every k there are k such points that are collinear. By considering the convex hull of the prime number graph, we show that there are infinitely many n such that 2pn < pn_¡ + Pn+Ifor all positive i < n. By a similar argument, we show that there are infinitely many n for which pn > ...
متن کاملThe Prime Number Formulas
There are many proposed partial prime number formulas, however, no formula can generate all prime numbers. Here we show three formulas which can obtain the entire prime numbers set from the positive integers, based on the Möbius function plus the “omega” function, or the Omega function, or the divisor function. The history of searching for a prime number formula goes back to the ancient Egyptia...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2020
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/7996