### Abstract

In 1742, Goldbach and Euler in conversation and in an exchange of letters discussed the representation of numbers as sums of at most three primes. Although the question as to whether every even number is the sum of one or two primes (the binary Goldbach conjecture) is still unresolved, this and associated questions have attracted many mathematicians over the years, and have lead to a range of powerful techniques with many applications. This article is a commentary on the historical developments, the underlying key ideas and their widespread influence on a variety of central questions.

Original language | English (US) |
---|---|

Title of host publication | Open Problems in Mathematics |

Publisher | Springer International Publishing |

Pages | 479-520 |

Number of pages | 42 |

ISBN (Electronic) | 9783319321622 |

ISBN (Print) | 9783319321608 |

DOIs | |

State | Published - Jan 1 2016 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Economics, Econometrics and Finance(all)
- Business, Management and Accounting(all)

### Cite this

*Open Problems in Mathematics*(pp. 479-520). Springer International Publishing. https://doi.org/10.1007/978-3-319-32162-2_16

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*Open Problems in Mathematics.*Springer International Publishing, pp. 479-520. https://doi.org/10.1007/978-3-319-32162-2_16

**Goldbach’s conjectures : A historical perspective.** / Vaughan, Robert C.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Goldbach’s conjectures

T2 - A historical perspective

AU - Vaughan, Robert C.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In 1742, Goldbach and Euler in conversation and in an exchange of letters discussed the representation of numbers as sums of at most three primes. Although the question as to whether every even number is the sum of one or two primes (the binary Goldbach conjecture) is still unresolved, this and associated questions have attracted many mathematicians over the years, and have lead to a range of powerful techniques with many applications. This article is a commentary on the historical developments, the underlying key ideas and their widespread influence on a variety of central questions.

AB - In 1742, Goldbach and Euler in conversation and in an exchange of letters discussed the representation of numbers as sums of at most three primes. Although the question as to whether every even number is the sum of one or two primes (the binary Goldbach conjecture) is still unresolved, this and associated questions have attracted many mathematicians over the years, and have lead to a range of powerful techniques with many applications. This article is a commentary on the historical developments, the underlying key ideas and their widespread influence on a variety of central questions.

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UR - http://www.scopus.com/inward/citedby.url?scp=85053744582&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-32162-2_16

DO - 10.1007/978-3-319-32162-2_16

M3 - Chapter

AN - SCOPUS:85053744582

SN - 9783319321608

SP - 479

EP - 520

BT - Open Problems in Mathematics

PB - Springer International Publishing

ER -