ZetaGrid was at one time the largest

distributed computing Distributed computing is a field of computer science that studies distributed systems, defined as computer systems whose inter-communicating components are located on different networked computers. The components of a distributed system commu ...

project, designed to explore the non-trivial

root In vascular plants, the roots are the plant organ, organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often bel ...

s of the

Riemann zeta function The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for and its analytic c ...

, checking over one billion roots a day. Roots of the zeta function are of particular interest in

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

; a single root out of alignment would disprove the

Riemann hypothesis In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important unsolved problem in pure ...

, with far-reaching consequences for all of mathematics. The project ended in November 2005 due to instability of the hosting provider. The first more than 10¹³ zeroes were checked. The project administrator stated that after the results were analyzed, they would be posted on the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

website. The official status remains unclear, however, as it was never published nor independently verified. This is likely because there was no evidence that each zero was actually computed, as there was no process implemented to check each one as it was calculated.Yannick Saouter and Patrick Demichel. A sharp region where π(x)−li(x) is positive. Math. Comp. 79 (2010) 2398. MR 2684372.

References

External links

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Grid computing Zeta and L-functions Hilbert's problems Experimental mathematics {{math-hist-stub