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Number theory --- Numbers, Prime --- Numbers, Prime.

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Computer. Automation --- Number theory --- Factorization (Mathematics) --- Numbers, Prime --- Numbers, Prime. --- Factorization (Mathematics). --- Nombres premiers. --- Algorithmes. --- Algorithms. --- Algorithmes --- Nombres premiers --- Nombres, Théorie des

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On August 6, 2002,a paper with the title “PRIMES is in P”, by M. Agrawal, N. Kayal, and N. Saxena, appeared on the website of the Indian Institute of Technology at Kanpur, India. In this paper it was shown that the “primality problem”hasa“deterministic algorithm” that runs in “polynomial time”. Finding out whether a given number n is a prime or not is a problem that was formulated in ancient times, and has caught the interest of mathema- ciansagainandagainfor centuries. Onlyinthe 20thcentury,with theadvent of cryptographic systems that actually used large prime numbers, did it turn out to be of practical importance to be able to distinguish prime numbers and composite numbers of signi?cant size. Readily, algorithms were provided that solved the problem very e?ciently and satisfactorily for all practical purposes, and provably enjoyed a time bound polynomial in the number of digits needed to write down the input number n. The only drawback of these algorithms is that they use “randomization” — that means the computer that carries out the algorithm performs random experiments, and there is a slight chance that the outcome might be wrong, or that the running time might not be polynomial. To ?nd an algorithmthat gets by without rand- ness, solves the problem error-free, and has polynomial running time had been an eminent open problem in complexity theory for decades when the paper by Agrawal, Kayal, and Saxena hit the web.

Number theory. --- Algebra. --- Algorithms. --- Computers. --- Data encryption (Computer science). --- Mathematical statistics. --- Numbers, Prime. --- Polynomials. --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Data encoding (Computer science) --- Encryption of data (Computer science) --- Computer security --- Cryptography --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Mathematical analysis --- Number study --- Numbers, Theory of --- Algebra --- Prime numbers --- Numbers, Natural --- Algorism --- Arithmetic --- Statistical methods --- Foundations --- Numbers, Prime --- Algorithms --- Computer science. --- Cryptography. --- Computer science --- Number Theory. --- Theory of Computation. --- Cryptology. --- Probability and Statistics in Computer Science. --- Mathematics. --- Informatics --- Science --- Computer mathematics --- Electronic data processing --- Cryptanalysis --- Cryptology --- Secret writing --- Steganography --- Signs and symbols --- Symbolism --- Writing --- Ciphers --- Data encryption (Computer science) --- Polynomials --- Polynômes --- Nombres premiers --- Algorithmes --- EPUB-LIV-FT SPRINGER-B

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Social law. Labour law --- Belgium --- arbeidsrecht --- loonpremie --- droit du travail --- prime de salaire --- premia --- prémie --- προσαυξήσεις μισθού --- паричен бонус --- preemia --- jutalom --- bonus payment --- pagesë shtesë --- премия --- premio salariale --- prima salarial --- plata primelor --- новчана награда уз плату --- prēmiju izmaksa --- pagament tal-bonus --- prémio salarial --- novčana nagrada za rad --- premija --- bonus --- Gehaltsprämie --- dodatno nagrajevanje --- επίδομα πολυετίας --- tryliktasis atlyginimas --- tillägg --- trīspadsmitā alga --- Festsetzung der Prämien --- shpërblim vjetërsie --- prēmija --- osobní ohodnocení --- ikälisä --- 13. plaća --- priemokų sistema --- gada noslēguma piemaksa --- kolmeteistkümnes palk --- premie --- priemokos nustatymas --- piemaksa par stāžu --- bonusfastsættelse --- årsbonus --- eindejaarspremie --- bonus determination --- prime de fin d'année --- premija prie darbo užmokesčio --- odmena --- end of year bonus --- primă de vechime --- додаток на плата за кариера --- систем за наградување --- vaststelling van premies --- anciennitetstillæg --- καθορισμός προσαυξήσεων --- metinė premija --- trettende månedsløn --- dreizehntes Monatsgehalt --- καθεστώς προσαυξήσεων --- επιμίσθιο --- osobní příplatek --- bonussystem --- paga extra --- rroga e trembëdhjetë --- tredicesima mensilità --- prémio de antiguidade --- bonusjärjestelmä --- trinásty plat --- premio di fine anno --- përcaktim i shpërblimit --- piemaksu noteikšana --- určenie prémií --- Prämiensystem --- premio di anzianità --- premio --- věrnostní příplatek --- wage premium --- extra månadslön --- premēšanas sistēma --- Weihnachtsgratifikation --- fastställande av bonus --- kerstgratificatie --- δέκατος τρίτος μισθός --- тринаесетта плата --- prémium --- régime de prime --- shpërblim i fundvitit --- sikerdíj --- stabilire prime --- mzdový příplatek --- mimořádná odměna --- božićnica --- kuukauden ylimääräinen palkka --- primă de sfârșit de an --- aastapreemia --- seniority bonus --- επίδομα --- ekstra månedsløn --- bonificação salarial --- prima --- regime dos prémios --- lisapalk --- jubilarna nagrada --- lisatasude süsteem --- piemaksa pie algas --- systém prémií --- bonusten määrittäminen --- anciennitetstillägg --- Dienstalterszulage --- preemiate määramine --- nagrada za dugogodišnji rad --- mzdová prémia --- premio di produzione --- jutalmazási rend --- reward --- sobresueldo --- stimulacija --- Alterszulage --- mzdová prémie --- Alterszuschlag --- lisäkorvaus --- Gratifikation --- čtrnáctý plat --- fissazione del premio --- prémia za odpracované roky --- tizenharmadik havi illetmény --- bonusordning --- julgratifikation --- vuosibonus --- prim i pagës --- jubileumi jutalom --- incentivo --- koncoročné prémie --- lisatasu --- gratificación --- belønning --- al treisprezecelea salariu --- prima de antigüedad --- regime dei premi --- régimen de prima --- prime --- prémio --- 13. havi illetmény --- thirteenth month's salary --- fixação do prémio --- décimo terceiro mês --- fijación de prima --- recompensă --- Gehaltszulage --- třináctý plat --- bonus system --- dertiende maand --- Prämienlohnsystem --- fixation de prime --- Zuschlag --- premiestelsel --- prime d'ancienneté --- dienstjarenpremie --- priemoka už gerą darbą --- premijinė išmoka --- treizième mois --- lisäpalkka --- Sonderzuwendung --- sistem de prime --- priemoka už darbo stažą --- sistem i shpërblimit --- εργατικό δίκαιο --- Arbeitsrecht --- munkajog --- radno pravo --- arbejdsret --- prawo pracy --- pracovní právo --- трудово право --- радно право --- labour law --- työoikeus --- dlí an tsaothair --- direito do trabalho --- Derecho del trabajo --- diritto del lavoro --- darbo teisė --- arbetsrätt --- delovno pravo --- liġi tax-xogħol --- e drejta e punës --- tööõigus --- darba tiesības --- pracovné právo --- dreptul muncii --- arbetslagstiftning --- employment law --- засновање работен однос --- disciplina giuridica del lavoro --- droits du travailleur --- трудово законодавство --- εργατική νομοθεσία --- statuto dei lavoratori --- legislazione del lavoro --- munkavállalók joga --- munkaügyi jogszabályok --- tutela dei lavoratori --- pracovní legislativa --- nodarbināto tiesības --- kolektivní pracovní právo --- direitos do trabalhador --- legislación laboral --- radno zakonodavstvo --- δικαιώματα των εργαζομένων --- työlainsäädäntö --- arbetstagarens rättigheter --- të drejtat e punonjësve --- diritti del lavoratore --- legislação do trabalho --- darbo įstatymai --- Derecho laboral --- estatuto de los trabajadores --- derechos del trabajador --- individuální pracovní právo --- tööseadusandlus --- legislación del trabajo --- darbininkų teisės --- drepturile salariaților --- darbinieka tiesības --- norme sul lavoro --- zákon o zaměstnanosti --- työntekijän oikeudet --- labour legislation --- darba tiesību akti --- workers' rights --- pracovnoprávna legislatíva --- arbejdstageres rettigheder --- práva pracujúcich --- legislația muncii --- munkaügyi jogalkotás --- Recht der Berufsausübung --- rechten van de arbeider --- pracovní zákon --- darba likumdošana --- arbejdslovgivning --- législation du travail --- arbeidswetgeving --- radnička prava --- töötaja õigused --- e drejta e punësimit --- права од работен однос --- laisvė dirbti --- legjislacion i punës --- Recht des Arbeitnehmers --- Arbeitsgesetzgebung --- íocaíocht bhónais

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"The P-NP problem is the most important open problem in computer science, if not all of mathematics. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. But difficulty also has its advantages. Hard problems allow us to safely conduct electronic commerce and maintain privacy in our online lives. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of the P-NP problem"--

Computer science --- NP-complete problems. --- Computer algorithms. --- Problems, NP-complete --- Computational complexity --- Algorithms --- NP-complete problems --- Computer algorithms --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- MATHEMATICS / Mathematical Analysis. --- MATHEMATICS / Linear Programming. --- MATHEMATICS / History & Philosophy. --- COMPUTERS / Programming / Algorithms. --- Facebook. --- Frenemy. --- Hamiltonian paths. --- Internet. --- Ketan Mulmuley. --- Leonid Levin. --- Martin Hellman. --- NP problem. --- NP problems. --- NP-complete. --- P versus NP problem. --- P versus NP. --- Richard Feynman. --- Steve Cook. --- Twitter. --- Urbana algorithm. --- Whitfield Diffie. --- academic work. --- algebraic geometry. --- algorithm. --- algorithms. --- approximation. --- big data. --- computational problems. --- computer science. --- computers. --- computing. --- cryptography. --- cryptosystem. --- database. --- decryption. --- digital computers. --- efficient algorithms. --- efficient computation. --- encryption. --- factoring. --- fast computers. --- graph isomorphism. --- heuristics. --- linear programming. --- mathematics. --- max-cut. --- network security. --- networking. --- new technologies. --- parallel computation. --- perebor. --- prime numbers. --- problems. --- programming. --- public-key cryptography. --- quantum computers. --- quantum computing. --- quantum cryptography. --- quantum mechanics. --- quantum physical systems. --- research community. --- secret messages. --- social networking data. --- solution. --- teleportation.