Primes in Progressions to Prime-Power Modulus.
Primes in Shart Intervals.
Primes in short arithmetic progressions
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 .
Primes of the form [cP].
Primes of the type φ(x, y)+A where φ is a quadratic form
Primes, permutations and primitive roots.
Primes represented by quadratic polynomials in two variables
Primes which remain irreducible in a normal field
Primes with preassigned digits
Primes with preassigned digits
Primes with preassigned digits II
Primitive divisors of certain elliptic divisibility sequences
Primitive divisors of Lucas and Lehmer sequences, II
Let and are conjugate complex algebraic integers which generate Lucas or Lehmer sequences. We present an algorithm to search for elements of such sequences which have no primitive divisors. We use this algorithm to prove that for all and with h, the -th element of these sequences has a primitive divisor for . In the course of proving this result, we give an improvement of a result of Stewart concerning more general sequences.
Primitive divisors of the expression An - Bn in algebraic number fields.
Primitive elements in integral bases
Primitive free quartics with specified norm and trace
Primitive lattice points in a thin strip along the boundary of a large convex planar domain