منابع مشابه
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...
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Let dn = Pn+i ~Pn denote the nth gap in the sequence of primes. We show that for every fixed integer A; and sufficiently large T the set of limit points of the sequence {(dn/logra, ■ • • ,dn+k-i/logn)} in the cube [0, T]k has Lebesgue measure > c(k)Tk, where c(k) is a positive constant depending only on k. This generalizes a result of Ricci and answers a question of Erdös, who had asked to prov...
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Many large arithmetic computations rely on tables of all primes less than n. For example, the fastest algorithms for computing n! takes time O(M(n logn) + P(n)), where M(n) is the time to multiply two n-bit numbers, and P(n) is the time to compute a prime table up to n. The fastest algorithm to compute ( n n/2 ) also uses a prime table. We show that it takes time O(M(n) + P(n)). In various mode...
متن کاملGenerating Prime Numbers
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We discuss a relative of the perfect numbers for which it is possible to prove that there are infinitely many examples. Call a natural number n prime-perfect if n and σ(n) share the same set of distinct prime divisors. For example, all even perfect numbers are prime-perfect. We show that the count Nσ(x) of prime-perfect numbers in [1, x] satisfies estimates of the form exp((log x) log log log )...
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ژورنال
عنوان ژورنال: Nature
سال: 1871
ISSN: 0028-0836,1476-4687
DOI: 10.1038/004006b0