A Diophantine property associated with prime twins.
A divisibility property of binomial coefficients viewed as an elementary sieve.
A natural prime-generating recurrence.
A necessary and sufficient condition for the primality of Fermat numbers
We examine primitive roots modulo the Fermat number . We show that an odd integer is a Fermat prime if and only if the set of primitive roots modulo is equal to the set of quadratic non-residues modulo . This result is extended to primitive roots modulo twice a Fermat number.
A new method in the elementary theory of primes
A Note on Formulae for the nth Prime.
A note on the extensions of Eratosthenes' sieve.
A sharp estimate of the number of integral points in a 4-dimensional tetrahedra.
A theorem of H. Steinhaus and -dense sets of positive integers
Abschätzung der Primalfunktion mit elementaren Methoden.
Addidtive representations of integers.
All elite primes up to 250 billion.
Aposyndesis in
We consider the Golomb and the Kirch topologies in the set of natural numbers. Among other results, we show that while with the Kirch topology every arithmetic progression is aposyndetic, in the Golomb topology only for those arithmetic progressions with the property that every prime number that divides also divides , it follows that being connected, being Brown, being totally Brown, and being aposyndetic are all equivalent. This characterizes the arithmetic progressions which are aposyndetic...
Appending digits to generate an infinite sequence of composite numbers.
Applications d'un corps fini dans lui-même
Approximation of by .
Aritmética de las sucesiones 6n-1,6n+1 y de los primos gemelos.
Aritmetika III – změny číslic vedoucí k prvočíslům aneb variace na Bertrandův postulát
Prvočísla a otázky s nimi spojené představují často jedny z nejtěžších problémů matematiky a mnohé z nich zůstávají stále otevřené. V tomto článku se zabýváme otázkou, jak blízko ke zvolenému číslu již můžeme nalézt nějaké prvočíslo. Na základě známých tvrzení lze vyslovit hypotézu, že z každého přirozeného čísla lze již změnou nejvýše dvou číslic získat prvočíslo. Úvahy, kterými rozvíjíme známé výsledky, jsou čistě aritmetické povahy. Vyslovená hypotéza, která je závislá na hypotéze z (Hanson,...
Asymptotic order of the square-free part of .
Automaticity IV : sequences, sets, and diversity
This paper studies the descriptional complexity of (i) sequences over a finite alphabet ; and (ii) subsets of (the natural numbers). If is a sequence over a finite alphabet , then we define the -automaticity of , to be the smallest possible number of states in any deterministic finite automaton that, for all with , takes expressed in base as input and computes . We give examples of sequences that have high automaticity in all bases ; for example, we show that the characteristic...