zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Totally Goldbach numbers and related conjectures. (English) Zbl 1162.11383

Goldbach’s famous conjecture is that every even integer n greater than 2 is the sum of two primes; to date it has been verified for n up to 10 17 ; see [T. Oliveira e Silva, “Goldbach conjecture verification”, web page, http://www.ieeta.pt/~tos/goldbach.html, J. Richstein, Math. Comput. 70, 1745–1749 (2001; Zbl 0989.11050)]. In order to establish the conjecture for a given even integer n, one optimistic approach is to simply choose a prime p<n, and check to see whether n-p is prime. Of course, one has to make a sensible choice of p; if n-1 is prime, one should not choose p=n-1, and there is obviously no point choosing a prime p which is a factor of n.

In this paper we examine the set of numbers n for which every “sensible choice” of p works:

Definition: A positive integer n is totally Goldbach if for all primes p<n-1 with p not dividing n, we have that n-p is prime. We denote by A the set of all totally Goldbach numbers.

Four conjectures are stated.

11P32Additive questions involving primes