Prime divisors of -binomial coefficients
Prime divisors of some shifted products.
Prime facto rs of consecutive integers.
Prime Factorization of Sums and Differences of Two Like Powers
Representation of a non zero integer as a signed product of primes is unique similarly to its representations in various types of positional notations [4], [3]. The study focuses on counting the prime factors of integers in the form of sums or differences of two equal powers (thus being represented by 1 and a series of zeroes in respective digital bases). Although the introduced theorems are not particularly important, they provide a couple of shortcuts useful for integer factorization, which could...
Prime factors of binomial coefficients and related problems
Prime k-th power non-residues
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 such that the sums of the divisors of their powers are perfect power numbers
Prime numbers such that the sums of the divisors of their powers are perfect squares
Prime numbers with a fixed number of one bits or zero bits in their binary representation.
Prime Pythagorean triangles.
Prime values of irreducible polynomials
Primes in classes of the iterated totient function.
Primes in Fibonacci -step and Lucas -step sequences.
Primes in intervals
Primes of the form .
Primes, permutations and primitive roots.
Primes with preassigned digits
Primitive free quartics with specified norm and trace
Primitive Lucas d-pseudoprimes and Carmichael-Lucas numbers
Let d be a fixed positive integer. A Lucas d-pseudoprime is a Lucas pseudoprime N for which there exists a Lucas sequence U(P,Q) such that the rank of appearance of N in U(P,Q) is exactly (N-ε(N))/d, where the signature ε(N) = (D/N) is given by the Jacobi symbol with respect to the discriminant D of U. A Lucas d-pseudoprime N is a primitive Lucas d-pseudoprime if (N-ε(N))/d is the maximal rank of N among Lucas sequences U(P,Q) that exhibit N as a Lucas pseudoprime. We derive...