Goldbachn.

Brit.

/ˈɡəʊldbɑːk/,

/ˈɡəʊldbɑːx/, U.S.

/ˈɡoʊldˌbɑk/

Origin: From a proper name, combined with an English element. Etymons: proper name Goldbach , conjecture n.

Etymology: < the name of Christian Goldbach (1690–1764), German mathematician + conjecture n.

Mathematics.

attributive and in the genitive, esp. in Goldbach conjecture. Either of two conjectures of Goldbach regarding the expression of positive even numbers as the sums of prime numbers; esp. that every such number can be expressed as the sum of two prime numbers.In later use the conjecture that every positive even number can be expressed as the sum of two primes is sometimes called Goldbach's strong conjecture or the strong Goldbach conjecture, to distinguish it from a related conjecture that all odd numbers greater than seven can be expressed as the sum of three primes. This second conjecture (which follows from the first) is sometimes known as Goldbach's weak conjecture, the weak Goldbach conjecture, or Goldbach's ternary conjecture, and was proved to be true in 2013 by Peruvian mathematician Harald Helfgott.Goldbach's conjecture was first stated in correspondence between himself and Swiss mathematician Leonhard Euler (1707–83). For this reason, older literature often calls the conjecture the Goldbach–Euler conjecture (see quot. 1887).

ΘΚΠ

the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > specific conjecture

Goldbach1902

Riemann hypothesis1918

Waring's problem1920

Poincaré conjecture1938

Church's theorem1939

Church's thesis1954

1887 Johns Hopkins Univ. Circulars Apr. 27/1 Shortly before he [sc. Prof. Sylvester] died he was hopeful of being able to prove the Goldbach-Euler conjecture that every even number can be partitioned into two primes.]

1902 Bull. Amer. Math. Soc. 8 457 After an exhaustive discussion of Riemann's prime number formula, perhaps we may sometime be in a position to attempt the rigorous solution of Goldbach's problem.

1923 Math. Teacher 16 261 The Goldbach theorem for even numbers stands before us still as a challenge to our ingenuity.

1932 Amer. Math. Monthly 39 157 Euler definitely states that Goldbach had communicated to him the proposition (now known as Goldbach's conjecture).

1974 Philos. & Phenomenological Res. 34 599 It is impossible mathematically to prove a counter-example to Goldbach's conjectures.

1997 Jrnl. Number Theory 65 334 Goldbach's Ternary Conjecture..asserts that any odd number (≥9) can be expressed as a sum of three prime numbers.

2003 Amer. Math. Monthly 110 208 The strong Goldbach conjecture implies Erdős's conjecture.

2012 @AlgebraFact 20 Oct. in twitter.com (O.E.D. Archive) Vinogradov proved there are at most a finite number of exceptions to the Goldbach conjecture.

Compounds

Goldbach number n. any positive even number that can be expressed as the sum of two odd prime numbers.

ΚΠ

1958 Math. Gaz. 42 10 If any even integer is written in the binary scale, then it is possible to convert it into a ‘Goldbach number’ by changing at most c₉ digits.

1990 Glasgow Math. Jrnl. 32 286 Almost all even numbers are Goldbach numbers.

2013 J. Pintz in L. Lováz et al. Erdős Centennial 506 Due to the similarity with Goldbach numbers, one gets the impression that the results which we can show for Goldbach and Maillet numbers are completely analogous.

Goldbach partition n. any pair of odd prime numbers whose sum is equal to a given even number.

ΚΠ

1975 BIT 15 239 The number of Goldbach partitions has been computed for all even numbers ≤ 350,000.

2010 C. Foster Resources for Teaching Math. xl. 169 A good task is to write out ‘Goldbach partitions’ for the positive integers up to 20.

This entry has been updated (OED Third Edition, December 2018; most recently modified version published online March 2022).

单词	goldbach
释义	Goldbachn. Brit. /ˈɡəʊldbɑːk/, /ˈɡəʊldbɑːx/, U.S. /ˈɡoʊldˌbɑk/ Origin: From a proper name, combined with an English element. Etymons: proper name Goldbach , conjecture n. Etymology: < the name of Christian Goldbach (1690–1764), German mathematician + conjecture n. Mathematics. attributive and in the genitive, esp. in Goldbach conjecture. Either of two conjectures of Goldbach regarding the expression of positive even numbers as the sums of prime numbers; esp. that every such number can be expressed as the sum of two prime numbers.In later use the conjecture that every positive even number can be expressed as the sum of two primes is sometimes called Goldbach's strong conjecture or the strong Goldbach conjecture, to distinguish it from a related conjecture that all odd numbers greater than seven can be expressed as the sum of three primes. This second conjecture (which follows from the first) is sometimes known as Goldbach's weak conjecture, the weak Goldbach conjecture, or Goldbach's ternary conjecture, and was proved to be true in 2013 by Peruvian mathematician Harald Helfgott.Goldbach's conjecture was first stated in correspondence between himself and Swiss mathematician Leonhard Euler (1707–83). For this reason, older literature often calls the conjecture the Goldbach–Euler conjecture (see quot. 1887). ΘΚΠ the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > specific conjecture Goldbach1902 Riemann hypothesis1918 Waring's problem1920 Poincaré conjecture1938 Church's theorem1939 Church's thesis1954 1887 Johns Hopkins Univ. Circulars Apr. 27/1 Shortly before he [sc. Prof. Sylvester] died he was hopeful of being able to prove the Goldbach-Euler conjecture that every even number can be partitioned into two primes.] 1902 Bull. Amer. Math. Soc. 8 457 After an exhaustive discussion of Riemann's prime number formula, perhaps we may sometime be in a position to attempt the rigorous solution of Goldbach's problem. 1923 Math. Teacher 16 261 The Goldbach theorem for even numbers stands before us still as a challenge to our ingenuity. 1932 Amer. Math. Monthly 39 157 Euler definitely states that Goldbach had communicated to him the proposition (now known as Goldbach's conjecture). 1974 Philos. & Phenomenological Res. 34 599 It is impossible mathematically to prove a counter-example to Goldbach's conjectures. 1997 Jrnl. Number Theory 65 334 Goldbach's Ternary Conjecture..asserts that any odd number (≥9) can be expressed as a sum of three prime numbers. 2003 Amer. Math. Monthly 110 208 The strong Goldbach conjecture implies Erdős's conjecture. 2012 @AlgebraFact 20 Oct. in twitter.com (O.E.D. Archive) Vinogradov proved there are at most a finite number of exceptions to the Goldbach conjecture. Compounds Goldbach number n. any positive even number that can be expressed as the sum of two odd prime numbers. ΚΠ 1958 Math. Gaz. 42 10 If any even integer is written in the binary scale, then it is possible to convert it into a ‘Goldbach number’ by changing at most c₉ digits. 1990 Glasgow Math. Jrnl. 32 286 Almost all even numbers are Goldbach numbers. 2013 J. Pintz in L. Lováz et al. Erdős Centennial 506 Due to the similarity with Goldbach numbers, one gets the impression that the results which we can show for Goldbach and Maillet numbers are completely analogous. Goldbach partition n. any pair of odd prime numbers whose sum is equal to a given even number. ΚΠ 1975 BIT 15 239 The number of Goldbach partitions has been computed for all even numbers ≤ 350,000. 2010 C. Foster Resources for Teaching Math. xl. 169 A good task is to write out ‘Goldbach partitions’ for the positive integers up to 20. This entry has been updated (OED Third Edition, December 2018; most recently modified version published online March 2022). < n.1902
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