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The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP ...
10 15 = 1,000,000,000,000,000 = 1 million billion = 1 ... One solution to the problem of comparing large numbers ... Certain fields of mathematics define infinite ...
The Yang–Mills existence and mass gap problem is an unsolved problem in mathematical physics and mathematics, and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute, which has offered a prize of US$1,000,000 for its solution. The problem is phrased as follows: [1] Yang–Mills Existence and Mass Gap.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Unlike the Hilbert problems, where the primary award was the admiration of Hilbert in particular and mathematicians in general, each prize problem includes a million-dollar bounty. As with the Hilbert problems, one of the prize problems (the Poincaré conjecture) was solved relatively soon after the problems were announced.
By 1 May 2006, VanLandingham had reached the 300 million digit mark (at a rate of one million digits every 5 to 7 days). Using distributed processing, [10] in 2011 Romain Dolbeau completed a billion iterations to produce a number with 413,930,770 digits, and in February 2015 his calculations reached a number with a billion digits. [11]
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Million Million Million M Mega-2 1 10 9: Billion Thousand million Milliard G Giga-3 2 10 12: Trillion Billion Billion T Tera-4 2 10 15: Quadrillion Thousand billion Billiard P Peta-5 3 10 18: Quintillion Trillion Trillion E Exa-6 3 10 21: Sextillion Thousand trillion Trilliard Z Zetta-7 4 10 24: Septillion Quadrillion Quadrillion Y Yotta-8 4 10 ...