Primality testing algorithms
Primality tests using algebraic groups.
Prime constellations in triangles with binomial coefficient congruences
The primality of numbers, or of a number constellation, will be determined from residue solutions in the simultaneous congruence equations for binomial coefficients found in Pascal’s triangle. A prime constellation is a set of integers containing all prime numbers. By analyzing these congruences, we can verify the primality of any number. We present different arrangements of binomial coefficient elements for Pascal’s triangle, such as by the row shift method of Mann and Shanks and especially by...
Prime divisors of polynomials at consecutive integers.
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 .