Related papers: Pseudoprimes stronger than strong pseudoprimes
We consider several problems about pseudoprimes. First, we look at the issue of their distribution in residue classes. There is a literature on this topic in the case that the residue class is coprime to the modulus. Here we provide some…
In this work we present a natural generalization of strong pseudoprime to base $b$, which we have called $q$-pseudoprime to base $b$. It allows us to present another way to define a Midy's number to base $b$ (overpseudoprime to base $b$).…
We introduce a new class of pseudoprimes-so called "overpseudoprimes to base $b$", which is a subclass of strong pseudoprimes to base $b$. Denoting via $|b|_n$ the multiplicative order of $b$ modulo $n$, we show that a composite $n$ is…
We introduce a new class of pseudoprimes-so called "overpseudoprimes" which is a special subclass of super-Poulet pseudoprimes. Denoting via h(n) the multiplicative order of 2 modulo n, we show that odd number n is overpseudoprime iff value…
The proliferation of probable prime tests in recent years has produced a plethora of definitions with the word ``pseudoprime'' in them. Examples include pseudoprimes, Euler pseudoprimes, strong pseudoprimes, Lucas pseudoprimes, strong Lucas…
Carmichael showed for sufficiently large $L$, that $F_L$ has at least one prime divisor that is $\pm 1({\rm mod}\, L)$. For a given $F_L$, we will show that a product of distinct odd prime divisors with that congruence condition is a…
In this note, we prove $p^2$ is a Morley pseudoprime (of order 2) iff $p^2$ is a Wolstenholme pseudoprime (of order 2) iff $p$ is a Wolstenholme prime iff $p$ is a Morley prime. Concerning pseudoprimes of order 1 that are not powers of…
Let $\psi_m$ be the smallest strong pseudoprime to the first $m$ prime bases. This value is known for $1 \leq m \leq 11$. We extend this by finding $\psi_{12}$ and $\psi_{13}$. We also present an algorithm to find all integers $n\le B$ that…
We give a complete characterization of pseudovarieties of semigroups whose finitely generated relatively free profinite semigroups are equidivisible. Besides the pseudovarieties of completely simple semigroups, they are precisely the…
We examine some properties of pseudo-multiplications, which are a special kind of associative binary relations defined on $\bar{\mathbb{R}}_+ \times \bar{\mathbb{R}}_+$.
In this paper, we introduce a certain method to construct polynomials producing many absolute pseudoprimes. By this method, we give new polynomials producing absolute pseudoprimes with any fixed number of prime factors which can be viewed…
The supersymmetric product of a supercurve is constructed with the aid of a theorem of algebraic invariants and the notion of positive relative superdivisor (supervortex) is introduced. A supercurve of positive superdivisors of degree 1…
We provide a complete description of the category of pseudo-categories (including pseudo-functors, natural and pseudo-natural transformations and pseudo modifications). A pseudo-category is a non strict version of an internal category. It…
It's the age-old recurrence with a twist: sum the last two terms and if the result is composite, divide by its smallest prime divisor to get the next term (e.g., 0, 1, 1, 2, 3, 5, 4, 3, 7, ...). These sequences exhibit pseudo-random…
Inside the symmetric product of a very general curve, we consider the codimension-one subvarieties of symmetric tuples of points imposing exceptional secant conditions on linear series on the curve of fixed degree and dimension. We compute…
We introduce extremely symmetric primes and provide some elementary properties of these.
The calculation of many and large Perrin pseudoprimes is a challenge. This is mainly due to their rarity. Perrin pseudoprimes are one of the rarest known pseudoprimes. In order to calculate many such large numbers, one needs not only a fast…
We construct a model in which the splitting number is large and every ultrafilter has a small subset with no pseudo-intersection.
Define $\psi_m$ to be the smallest strong pseudoprime to the first $m$ prime bases. The exact value of $\psi_m$ is known for $1\le m \le 8$. Z. Zhang have found a 19-decimal-digit number $Q_{11}=3825\,12305\,65464\,13051$ which is a strong…
In this paper we give a new semiprimality test and we construct a new formula for $\pi ^{(2)}(N)$, the function that counts the number of semiprimes not exceeding a given number $N$. We also present new formulas to identify the $n^{th}$…