Schinzel, Andrzej; Sierpiński, Wacław On certain hypotheses concerning prime numbers. (Sur certaines hypothèses concernant les nombres premiers.) (French) Zbl 0082.25802 Acta Arith. 4, 185-208 (1958). Beginnend mit der Erwähnung einiger bekannter Primzahlprobleme (Mersennesche Zahlen, Goldbach-Problem u. a.) geben die Verff. unter Hinzufügung neuer Hypothesen über dreißig Folgerungen an, die sich unter der Annahme der Richtigkeit dieser Primzahlvermutung herleiten lassen. Wegen der großen Zahl der Folgerungen muß auf die Arbeit selbst verwiesen werden. Reviewer: H. Ostmann Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 17 ReviewsCited in 51 Documents MSC: 11C08 Polynomials in number theory 11A41 Primes 11A51 Factorization; primality 11N05 Distribution of primes 11N32 Primes represented by polynomials; other multiplicative structures of polynomial values 11P32 Goldbach-type theorems; other additive questions involving primes Keywords:prime number theory; hypotheses; Schinzel hypothesis PDF BibTeX XML Cite \textit{A. Schinzel} and \textit{W. Sierpiński}, Acta Arith. 4, 185--208 (1958; Zbl 0082.25802) Full Text: DOI EuDML OpenURL Online Encyclopedia of Integer Sequences: Take minimal prime q such that n(q+1)-1 is prime (A060324), that is, the smallest prime q so that n = (p+1)/(q+1) with p prime; sequence gives values of p. Write the numbers from 1 to n^2 consecutively in n rows of length n; a(n) = minimal number of primes in a row. Products of exactly two supersingular primes (A002267). Smallest m > 0 such that there are no primes between n*m and n*(m+1) inclusive. The Schinzel-Sierpiński tree of fractions, read across levels. The Euclid tree with root 1 encoded by semiprimes, read across levels.