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
Primes with preassigned digits
Primes with preassigned digits II
Primzahlen der Gestalt [f (n)].
Problems and results on αp - βq
Products of integers in short intervals
Properties of some functions connected to prime numbers.
Properties of the function .
Prvočísla obsahují libovolně dlouhé aritmetické posloupnosti
Quadratic Residues and the Distribution of Prime Numbers.
Quelques applications de nouveaux résultats de van der Poorten
Quelques méthodes élémentaires en théorie des nombres
Rad prevrátených hodnôt všetkých prvočísel a niektoré výsledky o konvergencii čiastočných radov harmonického radu
Ramanujan-Fourier series and the conjecture D of Hardy and Littlewood
We give a heuristic proof of a conjecture of Hardy and Littlewood concerning the density of prime pairs to which twin primes and Sophie Germain primes are special cases. The method uses the Ramanujan-Fourier series for a modified von Mangoldt function and the Wiener-Khintchine theorem for arithmetical functions. The failing of the heuristic proof is due to the lack of justification of interchange of certain limits. Experimental evidence using computer calculations is provided for the plausibility...
Reductions of an elliptic curve with almost prime orders
Remarks on the differences between consecutive primes.