Examples of using Sum of two primes in English and their translations into Slovak
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Integers which are not the sum of two primes has density zero.
Problem: Sum of two primes- math problem(6808), natural numbers.
Every even integergreater than 2 can be written as the sum of two primes.
Every even number is a sum of two primes[Goldbach's conjecture].
Every even integergreater than 2 can be written as the sum of two primes.
Expressing a given even number as a sum of two primes is called a Goldbach partition of the number.
It states:Every even integer greater than 2 can be expressed as the sum of two primes.
("That… every even integer is a sum of two primes, I regard as a completely certain theorem, although I cannot prove it.")[7][8].
The set of even integers that are not the sum of two primes has density zero.
In 1975, Hugh Montgomery and Robert Charles Vaughan showedthat"most" even numbers are expressible as the sum of two primes.
Every integer that can be written as the sum of two primes, can also be written as the sum of as manyprimes as one wishes, until all terms are units.
It hypothesises that‘Everyeven integer greater than 2 can be expressed as the sum of two primes.'.
Since 4 is the only even number greater than 2 that requires the even prime 2 in order tobe written as the sum of two primes, another form of the statement of Goldbach's conjecture is that all even integers greater than 4 are Goldbach numbers.
More precisely, they showed that there existed positive constant c, C such that for all sufficiently large numbers N,every even number less than N is the sum of two primes, with at most CN1- c exceptions.
Since four is the only even number greater than two that requires the even prime 2 in order tobe written as the sum of two primes, another form of the statement of Goldbach's conjecture is that all even integers greater than 4 are Goldbach numbers.
Euler replied in a letter dated 30 June 1742, and reminded Goldbach of an earlier conversation they had("… so Ew vormals mit mir communicirt haben…"), in which Goldbach remarked his original(and not marginal) conjecture followed from the following statement Every even integergreater than 2 can be written as the sum of two primes, which is, thus, also a conjecture of Goldbach.
The number of ways in which 2n can be written as the sum of two primes(for n starting at 1) is.
Linnik proved in 1951 the existence of a constant K such that everysufficiently large even number is the sum of two primes and at most K powers of 2.
Using Vinogradov's method, Chudakov, Van der Corput, and Estermann showed that almost alleven numbers can be written as the sum of two primes(in the sense that the fraction of even numbers which can be so written tends towards 1).
More precisely, they showed that there exist positive constants c and C such that for all sufficiently large numbers N,every even number less than N is the sum of two primes, with at most C N 1- c{\displaystyle CN^{1-c}} exceptions.
The strong Goldbach conjecture is much more difficult than the weak Goldbach conjecture. Using Vinogradov's method, Chudakov,[14] Van der Corput,[15] and Estermann[16]showed that almost all even numbers can be written as the sum of two primes(in the sense that the fraction of even numbers which can be so written tends towards 1).
On 7 June 1742, the German mathematician Christian Goldbach wrote a letter to Leonhard Euler(letter XLIII) in which he proposed the following conjecture:Every integer which can be written as the sum of two primes, can also be written as the sum of as many primes as one wishes, until all terms are units.