# Bombieri, E. "Problems of the Millennium: The Riemann Hypothesis." .

In the Season 1 episode "" (2005) of the television crime drama , math genius Charlie Eppes realizes that character Ethan's daughter has been kidnapped because he is close to solving the Riemann hypothesis, which allegedly would allow the perpetrators to break essentially all internet security.

## Clay Mathematics Institute. "The Riemann Hypothesis." .

### Conrey, J. B. "The Riemann Hypothesis." 50,341-353, 2003. .

According to Fields medalist Enrico Bombieri, "The failure of the Riemann hypothesis would create havoc in the distribution of prime numbers" (Havil 2003, p. 205).

### That is the Riemann Hypothesis.

In Ron Howard's 2001 film , John Nash (played by Russell Crowe) is hindered in his attempts to solve the Riemann hypothesis by the medication he is taking to treat his schizophrenia.

## The Riemann Hypothesis For Dummies @ Things Of …

The Riemann hypothesis was computationally tested and found to be true for the first zeros by Brent (1982), covering zeros in the region ). S. Wedeniwski used ZetaGrid () to prove that the first trillion () nontrivial zeros lie on the . Gourdon (2004) then used a faster method by Odlyzko and Schönhage to verify that the first ten trillion () nontrivial zeros of the function lie on the . This computation verifies that the Riemann hypothesis is true at least for all less than 2.4 trillion. These results are summarized in the following table, where indicates a .

## What does proving the Riemann Hypothesis accomplish?

André Weil proved the Riemann hypothesis to be true for field functions (Weil 1948, Eichler 1966, Ball and Coxeter 1987). In 1974, Levinson (1974ab) showed that at least 1/3 of the must lie on the (Le Lionnais 1983), a result which has since been sharpened to 40% (Vardi 1991, p. 142). It is known that the zeros are symmetrically placed about the line . This follows from the fact that, for all complex numbers ,

### The Riemann hypothesis is true according to the axiom.

While it was long believed that Riemann's hypothesis was the result of deep intuition on the part of Riemann, an examination of his papers by C. L. Siegel showed that Riemann had made detailed numerical calculations of small zeros of the to several decimal digits (Granville 2002; Borwein and Bailey 2003, p. 68).

### Perry's introductory notes on the Riemann HypothesisP.

The Riemann hypothesis has thus far resisted all attempts to prove it. Stieltjes (1885) published a note claiming to have proved the with , a result stronger than the Riemann hypothesis and from which it would have followed. However, the proof itself was never published, nor was it found in Stieltjes papers following his death (Derbyshire 2004, pp. 160-161 and 250). Furthermore, the Mertens conjecture has been proven false, completely invalidating this claim. In the late 1940s, H. Rademacher's erroneous proof of the falsehood of Riemann's hypothesis was reported in magazine, even after a flaw in the proof had been unearthed by Siegel (Borwein and Bailey 2003, p. 97; Conrey 2003). de Branges has written a number of papers discussing a potential approach to the (de Branges 1986, 1992, 1994) and in fact claiming to prove the generalized Riemann hypothesis (de Branges 2003, 2004; Boutin 2004), but no actual proofs seem to be present in these papers. Furthermore, Conrey and Li (1998) prove a counterexample to de Branges's approach, which essentially means that theory developed by de Branges is not viable.

### Riemann Hypothesis -- from Wolfram MathWorld

In 2000, the Clay Mathematics Institute () offered a \$1 million prize () for proof of the Riemann hypothesis. Interestingly, of the Riemann hypothesis (e.g., by using a computer to actually find a zero off the ), does not earn the \$1 million award.