in short intervals
For any sufficiently large real number , the interval contains at least one integer having at most two prime factors .
p+a without large prime factors.
Perfect powers in products of integers from a block of consecutive integers
Potenzfreie Werte von Polynomen in algebraischen Zahlkörpern.
Prime divisors of polynomials at consecutive integers.
Prime facto rs of consecutive integers.
Prime numbers along Rudin–Shapiro sequences
For a large class of digital functions , we estimate the sums (and , where denotes the von Mangoldt function (and the Möbius function). We deduce from these estimates a Prime Number Theorem (and a Möbius randomness principle) for sequences of integers with digit properties including the Rudin-Shapiro sequence and some of its generalizations.
Prime numbers in short intervals
Prime numbers of the form p = m²+n²+1 in short intervals
Prime percolation.
Primes and power-primes
Primes and zeros in short intervals.
Primes in almost all short intervals
Primes in almost all short intervals. II
In questo lavoro vengono migliorati i risultati ottenuti in «Primes in Almost All Short Intervals» riguardo la distribuzione dei primi in quasi tutti gli intervalli corti della forma , con funzione reale appartenente ad una ampia classe di funzioni. Il problema viene trattato mettendo in relazione l'insieme eccezionale per la distribuzione dei primi in intervalli nella forma con l'insieme eccezionale per la formula asintotica I risultati presentati vengono quindi ottenuti grazie allo studio...
Primes in intervals
Primes in Shart Intervals.
Primes in Short Intervals.
Primes in tuples IV: Density of small gaps between consecutive primes
We prove that given any small but fixed η > 0, a positive proportion of all gaps between consecutive primes are smaller than η times the average gap. We show some unconditional and conditional quantitative results in this vein. In the results the dependence on η is given explicitly, providing a new quantitative way, in addition to that of the first paper in this series, of measuring the effect of the knowledge on the level of distribution of primes.
Primes of the form [cP].
Primes with preassigned digits