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5 unusual facts about Goldbach's conjecture


Banquets of the Black Widowers

"Sixty Million Trillion Combinations" (Ellery Queen's Mystery Magazine, 5 May 1980) – A paranoid mathematician who suspects that his work on Goldbach's conjecture has been stolen.

Constructive proof

One weak counterexample begins by taking some unsolved problem of mathematics, such as Goldbach's conjecture.

Goldbach's conjecture

This result was subsequently enhanced by many authors; currently, the best known result is due to Olivier Ramaré, who in 1995 showed that every even number n  ≥ 4 is in fact the sum of at most six primes.

Modal logic

From the other direction, Jones might say, (3) "It is possible that Goldbach's conjecture is true; but also possible that it is false", and also (4) "if it is true, then it is necessarily true, and not possibly false".

Olivier Ramaré

This result may be compared with Goldbach's conjecture, which states that every even number except 2 is the sum of two primes.


Beal's conjecture

Peter Norvig, Director of Research at Google, reported having conducted a series of numerical searches for counterexamples to Beal's conjecture.

Cathérine Hübscher

Catherine Hubscher (Goldbach-Altenbach, 2 February 1753 - 1835) was a First French Empire noblewoman, maréchale Lefebvre and duchesse de Dantzig by her marriage to François Joseph Lefebvre.

Christian Goldbach

Goldbach is most noted for his correspondence with Leibniz, Euler, and Bernoulli, especially in his 1742 letter to Euler stating his Goldbach's conjecture.

Crailsheim

The following boroughs comprise the Crailsheim municipality: Ingersheim, Altenmünster, Rotmühle, Tiefenbach, Onolzheim, Roßfeld, Jagstheim, Westgartshausen, Goldbach, Triensbach and Beuerlbach.

Firoozbakht’s conjecture

The conjecture is named after Farideh Firoozbakht, from the University of Isfahan, who stated it in 1982.

Goldbach, Bavaria

The sandstone Romanesque Revival church that stands today was built in 1894 and 1895 on the spot where once stood an older building that had become too small.

Goldbach's weak conjecture

In 2012 and 2013, Peruvian mathematician Harald Helfgott released a pair of papers claiming to improve major and minor arc estimates sufficiently to unconditionally prove the weak Goldbach conjecture.

Olivier Ramaré in 1995 showed that every even number n ≥ 4 is in fact the sum of at most six primes, from which it follows that every odd number n ≥ 5 is the sum of at most seven primes.

In 2013, Harald Helfgott claimed to have fully proved the conjecture for all odd integers greater than 5 (rather than the much larger e^{3100}\approx 2 \times 10^{1346}, implied by previous results).

Gustav Hegi

Gustav Hegi (13 November 1876 in Rickenbach, Canton of Zürich - 23 April 1932 in Goldbach, Canton of Zürich) was a Swiss botanist.

Jack Silver

Silver proved the consistency of Chang's conjecture using the Silver collapse (which is a variation of the Levy collapse).

Kato's conjecture

The problem remained unresolved for nearly a half-century, until it was jointly solved in 2001 by Pascal Auscher, Steve Hofmann, Michael Lacey, Alan McIntosh, and Philippe Tchamitchian.

Ke Zhao

Some of his major contributions included his work on quadratic forms, the Erdős–Ko–Rado theorem and his breakthrough on Catalan's conjecture.

Lemoine's conjecture

In number theory, Lemoine's conjecture, named after Émile Lemoine, also known as Levy's conjecture, after Hyman Levy, states that all odd integers greater than 5 can be represented as the sum of an odd prime number and an even semiprime.

The conjecture was posed by Émile Lemoine in 1895, but in more recent years came to be attributed to Hyman Levy who pondered it in the 1960s.

Logicomix

Logicomix: An Epic Search for Truth is a graphic novel about the foundational quest in mathematics, written by Apostolos Doxiadis, author of Uncle Petros and Goldbach's Conjecture, and theoretical computer scientist Christos Papadimitriou of the University of California, Berkeley.

Montanablue

Unfortunately being the critic's darlings did not translate into the kind of sales WEA had imagined and after releasing 2 more EP's on WEA and most importantly after the death of Conny Plank in 1987 the band lost any leverage it may have had and were dropped by WEA and Harold Goldbach.

Parity of zero

Before the 20th century, definitions of primality were inconsistent, and significant mathematicians such as Goldbach, Lambert, Legendre, Cayley, and Kronecker wrote that 1 was prime.

Pascal Auscher

Specializing in harmonic analysis and operator theory, he is mostly known for, together with Steve Hofmann, Michael Lacey, Alan McIntosh and Philippe Tchamitchian, solving the famous Kato's conjecture.

Paul Wolfskehl

Andrew Beal, a Dallas banker who has offered $100,000 for a proof or disproof of Beal's conjecture

Rajagopalan Parthasarathy

His work on the resolution of the Blattner's conjecture and the question of unitarisability of certain highest weight modules are significant contributions to this area in mathematics.

Sir Frederick Pollock, 1st Baronet

He contributed a number of papers in mathematics to the Royal Society, including one on what is now known as the Pollock's conjecture.

Stern prime

All the known Stern primes have more efficient Waring representations than their Goldbach representations would suggest.

Transcendence theory

Stephen Schanuel conjectured that the answer is n, but no proof is known.

Uncle Petros and Goldbach's Conjecture

Uncle Petros and Goldbach's Conjecture is a 1992 novel by Greek author Apostolos Doxiadis.


see also