as we mentioned before, many of the primality proving methods

8/14/2019 As We Mentioned Before, Many of the Primality Proving Methods

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http://primes.utm.edu/references/refs.cgi/Rabin80http://primes.utm.edu/references/refs.cgi/AH1992http://primes.utm.edu/references/refs.cgi/GK86http://primes.utm.edu/references/refs.cgi/AKS2002http://primes.utm.edu/prove/prove2_2.html#FLittleThttp://primes.utm.edu/prove/prove2_3.html#MillersERHTest


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http://primes.utm.edu/references/refs.cgi/AB1999http://primes.utm.edu/references/refs.cgi/BP2001http://primes.utm.edu/references/refs.cgi/KS2002


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http://primes.utm.edu/references/refs.cgi/AKS2002http://primes.utm.edu/references/refs.cgi/F1985http://primes.utm.edu/references/refs.cgi/BH1996http://primes.utm.edu/references/refs.cgi/Bernstein1998b


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http://primes.utm.edu/glossary/page.php?sort=SophieGermainPrimehttp://primes.utm.edu/references/refs.cgi/HL23http://primes.utm.edu/prove/prove4_2.htmlhttp://primes.utm.edu/prove/prove4_3.html#note1%23note1http://cr.yp.to/papers.html#akshttp://cr.yp.to/papers.html#akshttp://primes.utm.edu/references/refs.cgi/Berrizbeitia2003http://primes.utm.edu/references/refs.cgi/Cheng2003http://primes.utm.edu/references/refs.cgi/Bernstein2003


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http://www.instantlogic.net/publications/PRIMES%20is%20in%20P%20little%20FAQ.htmhttp://fatphil.org/maths/AKS/http://cr.yp.to/primetests.htmlhttp://cr.yp.to/primetests.htmlhttp://primes.utm.edu/prove/prove5.htmlhttp://primes.utm.edu/prove/prove4_2.htmlmailto:[email protected]://www.itl.nist.gov/div897/sqg/dads/HTML/polynomial.htmlhttp://www.itl.nist.gov/div897/sqg/dads/HTML/bigOnotation.htmlhttp://www.itl.nist.gov/div897/sqg/dads/HTML/sublinearTimeAlgo.htmlhttp://www.itl.nist.gov/div897/sqg/dads/HTML/np.htmlhttp://www.itl.nist.gov/div897/sqg/dads/HTML/exponential.htmlhttp://www.itl.nist.gov/div897/sqg/dads/HTML/logarithmic.htmlhttp://en.wikipedia.org/wiki/Subsethttp://en.wikipedia.org/wiki/NP_(complexity)http://en.wikipedia.org/wiki/Decision_problems


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http://en.wikipedia.org/wiki/Nondeterministic_Turing_machinehttp://en.wikipedia.org/wiki/If_and_only_ifhttp://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/P_%3D_NP_problemhttp://en.wikipedia.org/wiki/P_%3D_NP_problemhttp://en.wikipedia.org/w/index.php?title=NP-complete&action=edit&section=2http://en.wikipedia.org/wiki/P_%3D_NP_problem#Formal_definition_for_NP-completenesshttp://en.wikipedia.org/wiki/P_%3D_NP_problem#Formal_definition_for_NP-completenesshttp://en.wikipedia.org/wiki/Reduction_(complexity)http://en.wikipedia.org/wiki/Deterministic_algorithm


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http://en.wikipedia.org/wiki/NP-hardhttp://en.wikipedia.org/wiki/Universal_Turing_machinehttp://en.wikipedia.org/wiki/Turing-equivalenthttp://en.wikipedia.org/wiki/Abstract_machinehttp://en.wikipedia.org/wiki/Abstract_machinehttp://en.wikipedia.org/w/index.php?title=NP-complete&action=edit&section=3http://en.wikipedia.org/wiki/Stephen_Cookhttp://en.wikipedia.org/wiki/Stephen_Cookhttp://en.wikipedia.org/wiki/Complexityhttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Deterministichttp://en.wikipedia.org/wiki/Turing_machinehttp://en.wikipedia.org/wiki/John_Hopcrofthttp://en.wikipedia.org/wiki/John_Hopcrofthttp://en.wikipedia.org/wiki/Run_time_(computing)http://en.wikipedia.org/wiki/Unsolved_problems_of_mathematicshttp://en.wikipedia.org/wiki/Clay_Mathematics_Institutehttp://en.wikipedia.org/wiki/Clay_Mathematics_Institutehttp://en.wikipedia.org/wiki/Cook's_theoremhttp://en.wikipedia.org/wiki/Leonid_Levinhttp://en.wikipedia.org/wiki/Boolean_satisfiability_problemhttp://en.wikipedia.org/wiki/Boolean_satisfiability_problemhttp://en.wikipedia.org/wiki/Proof_that_Boolean_satisfiability_problem_is_NP-complete


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http://en.wikipedia.org/wiki/Proof_that_Boolean_satisfiability_problem_is_NP-completehttp://en.wikipedia.org/wiki/Richard_Karphttp://en.wikipedia.org/wiki/Karp's_21_NP-complete_problemshttp://en.wikipedia.org/wiki/Karp's_21_NP-complete_problemshttp://en.wikipedia.org/wiki/NP-complete#column-one%23column-onehttp://en.wikipedia.org/wiki/NP-complete#searchInput%23searchInputhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Complexity_classhttp://en.wikipedia.org/wiki/Polynomial_timehttp://en.wikipedia.org/wiki/NP_(complexity)


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http://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/List_of_open_problems_in_computer_sciencehttp://en.wikipedia.org/wiki/Computer_scientisthttp://en.wikipedia.org/wiki/Computer_scientisthttp://en.wikipedia.org/wiki/Computer_programmerhttp://en.wikipedia.org/wiki/Approximation_algorithmhttp://toggletoc%28%29/http://en.wikipedia.org/wiki/NP-complete#Formal_overview%23Formal_overviewhttp://en.wikipedia.org/wiki/NP-complete#Formal_definition_of_NP-completeness%23Formal_definition_of_NP-completenesshttp://en.wikipedia.org/wiki/NP-complete#Background%23Backgroundhttp://en.wikipedia.org/wiki/NP-complete#NP-complete_problems%23NP-complete_problemshttp://en.wikipedia.org/wiki/NP-complete#Solving_NP-complete_problems%23Solving_NP-complete_problemshttp://en.wikipedia.org/wiki/NP-complete#Completeness_under_different_types_of_reduction%23Completeness_under_different_types_of_reductionhttp://en.wikipedia.org/wiki/NP-complete#See_also%23See_alsohttp://en.wikipedia.org/wiki/NP-complete#References%23Referenceshttp://en.wikipedia.org/wiki/NP-complete#Further_reading%23Further_reading


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http://en.wikipedia.org/w/index.php?title=NP-complete&action=edit&section=1http://en.wikipedia.org/wiki/Subsethttp://en.wikipedia.org/wiki/NP_(complexity)http://en.wikipedia.org/wiki/Decision_problemshttp://en.wikipedia.org/wiki/Nondeterministic_Turing_machinehttp://en.wikipedia.org/wiki/If_and_only_ifhttp://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/P_%3D_NP_problemhttp://en.wikipedia.org/w/index.php?title=NP-complete&action=edit&section=2http://en.wikipedia.org/wiki/P_%3D_NP_problem#Formal_definition_for_NP-completenesshttp://en.wikipedia.org/wiki/Reduction_(complexity)http://en.wikipedia.org/wiki/Deterministic_algorithm


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http://en.wikipedia.org/wiki/NP-hardhttp://en.wikipedia.org/wiki/Universal_Turing_machinehttp://en.wikipedia.org/wiki/Turing-equivalenthttp://en.wikipedia.org/wiki/Abstract_machinehttp://en.wikipedia.org/w/index.php?title=NP-complete&action=edit&section=3http://en.wikipedia.org/wiki/Stephen_Cookhttp://en.wikipedia.org/wiki/Complexityhttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Deterministichttp://en.wikipedia.org/wiki/Turing_machinehttp://en.wikipedia.org/wiki/John_Hopcrofthttp://en.wikipedia.org/wiki/Run_time_(computing)http://en.wikipedia.org/wiki/Unsolved_problems_of_mathematicshttp://en.wikipedia.org/wiki/Clay_Mathematics_Institutehttp://en.wikipedia.org/wiki/Clay_Mathematics_Institutehttp://en.wikipedia.org/wiki/Cook's_theoremhttp://en.wikipedia.org/wiki/Leonid_Levinhttp://en.wikipedia.org/wiki/Boolean_satisfiability_problemhttp://en.wikipedia.org/wiki/Proof_that_Boolean_satisfiability_problem_is_NP-completehttp://en.wikipedia.org/wiki/Richard_Karphttp://en.wikipedia.org/wiki/Karp's_21_NP-complete_problems


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http://en.wikipedia.org/wiki/File:Relative_NPC_chart.PNGhttp://en.wikipedia.org/wiki/File:Relative_NPC_chart.PNGhttp://en.wikipedia.org/wiki/Gareyhttp://en.wikipedia.org/wiki/David_S._Johnsonhttp://en.wikipedia.org/w/index.php?title=NP-complete&action=edit&section=4http://en.wikipedia.org/wiki/List_of_NP-complete_problemshttp://en.wikipedia.org/wiki/Reduction_(complexity)http://en.wikipedia.org/wiki/Graph_isomorphism_problemhttp://en.wikipedia.org/wiki/Graph_theoryhttp://en.wikipedia.org/wiki/Graph_theoryhttp://en.wikipedia.org/wiki/Graph_isomorphismhttp://en.wikipedia.org/wiki/Isomorphichttp://en.wikipedia.org/wiki/Isomorphismhttp://en.wikipedia.org/wiki/Vertex_(graph_theory)


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http://en.wikipedia.org/wiki/Boolean_satisfiability_problemhttp://en.wikipedia.org/wiki/N-puzzlehttp://en.wikipedia.org/wiki/Knapsack_problemhttp://en.wikipedia.org/wiki/Hamiltonian_path_problemhttp://en.wikipedia.org/wiki/Travelling_salesman_problemhttp://en.wikipedia.org/wiki/Subgraph_isomorphism_problemhttp://en.wikipedia.org/wiki/Subset_sum_problemhttp://en.wikipedia.org/wiki/Clique_problemhttp://en.wikipedia.org/wiki/Vertex_cover_problemhttp://en.wikipedia.org/wiki/Independent_set_problemhttp://en.wikipedia.org/wiki/Dominating_set_problemhttp://en.wikipedia.org/wiki/Graph_coloring_problemhttp://en.wikipedia.org/wiki/Reduction_(complexity)http://en.wikipedia.org/wiki/3-satisfiabilityhttp://en.wikipedia.org/wiki/2-satisfiabilityhttp://en.wikipedia.org/wiki/NL-complete


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http://en.wikipedia.org/wiki/Planar_graphhttp://en.wikipedia.org/wiki/Cycle_graphhttp://en.wikipedia.org/wiki/Bipartite_graphhttp://en.wikipedia.org/wiki/L_(complexity)http://en.wikipedia.org/wiki/Knapsack_problemhttp://en.wikipedia.org/wiki/Knapsack_problemhttp://en.wikipedia.org/w/index.php?title=NP-complete&action=edit&section=5http://en.wikipedia.org/wiki/Superpolynomialhttp://en.wikipedia.org/wiki/Approximation_algorithmhttp://en.wikipedia.org/wiki/Randomized_algorithmhttp://en.wikipedia.org/wiki/Running_timehttp://en.wikipedia.org/wiki/Running_timehttp://en.wikipedia.org/wiki/Monte_Carlo_methodhttp://en.wikipedia.org/wiki/Parameterized_complexityhttp://en.wikipedia.org/wiki/Heuristic_(computer_science)http://en.wikipedia.org/wiki/Metaheuristichttp://en.wikipedia.org/wiki/Greedy_coloringhttp://en.wikipedia.org/wiki/Greedy_coloringhttp://en.wikipedia.org/wiki/Graph_coloring_problemhttp://en.wikipedia.org/wiki/Register_allocationhttp://en.wikipedia.org/wiki/Register_allocationhttp://en.wikipedia.org/w/index.php?title=Graph-coloring_global_register_allocation&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Graph-coloring_global_register_allocation&action=edit&redlink=1http://en.wikipedia.org/wiki/RISC


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http://en.wikipedia.org/wiki/Logarithmic_spacehttp://en.wikipedia.org/wiki/P-completehttp://en.wikipedia.org/w/index.php?title=NP-complete&action=edit&section=7http://en.wikipedia.org/wiki/List_of_NP-complete_problemshttp://en.wikipedia.org/wiki/Almost_completehttp://en.wikipedia.org/wiki/Ladner's_theoremhttp://en.wikipedia.org/wiki/Strongly_NP-completehttp://en.wikipedia.org/wiki/P_%3D_NP_problemhttp://en.wikipedia.org/wiki/NP-hard


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http://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Running_timehttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Computationhttp://en.wikipedia.org/wiki/Computerhttp://en.wikipedia.org/wiki/Abstract_machinehttp://en.wikipedia.org/wiki/Abstract_machinehttp://en.wikipedia.org/wiki/Upper_boundhttp://en.wikipedia.org/wiki/Polynomialhttp://en.wikipedia.org/wiki/Inputhttp://en.wikipedia.org/wiki/Decision_problemhttp://en.wikipedia.org/wiki/Complexity_classhttp://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/Computational_complexity_theory


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http://en.wikipedia.org/wiki/Problem_sizehttp://en.wikipedia.org/wiki/Polynomial_time#cite_note-1%23cite_note-1http://en.wikipedia.org/wiki/Polynomial_time#cite_note-2%23cite_note-2http://en.wikipedia.org/w/index.php?title=Polynomial_time&action=edit&section=2http://en.wikipedia.org/wiki/Optimization_(mathematics)http://en.wikipedia.org/wiki/Polynomial_time#cite_note-3%23cite_note-3


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http://en.wikipedia.org/wiki/Repeated_squaringhttp://en.wikipedia.org/wiki/Euclidean_algorithmhttp://en.wikipedia.org/wiki/Greatest_common_divisor


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http://en.wikipedia.org/wiki/Polynomial_time#cite_note-4%23cite_note-4http://en.wikipedia.org/wiki/Linear_programminghttp://en.wikipedia.org/wiki/Pseudo-polynomial_timehttp://en.wikipedia.org/w/index.php?title=Polynomial_time&action=edit&section=3http://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/Complexity_classhttp://en.wikipedia.org/wiki/Decision_problemhttp://en.wikipedia.org/wiki/P_(complexity)http://en.wikipedia.org/wiki/NP_(complexity)http://en.wikipedia.org/wiki/Non-deterministic_Turing_machinehttp://en.wikipedia.org/wiki/Non-deterministic_Turing_machinehttp://en.wikipedia.org/wiki/Robust#Computer_Engineeringhttp://en.wikipedia.org/wiki/Turing_machinehttp://en.wikipedia.org/wiki/Turing_machinehttp://en.wikipedia.org/wiki/Abstract_machinehttp://en.wikipedia.org/wiki/Abstract_machinehttp://en.wikipedia.org/wiki/Complexity_classhttp://en.wikipedia.org/w/index.php?title=Polynomial_time&action=edit&section=4http://en.wikipedia.org/wiki/Quicksort


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http://en.wikipedia.org/wiki/Abstract_machine#column-one%23column-onehttp://en.wikipedia.org/wiki/Abstract_machine#searchInput%23searchInputhttp://en.wikipedia.org/wiki/Computerhttp://en.wikipedia.org/wiki/Automata_theoryhttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Computer_engineeringhttp://en.wikipedia.org/wiki/Discrete_timehttp://en.wikipedia.org/wiki/Paradigmhttp://en.wikipedia.org/wiki/Theory_of_computationhttp://en.wikipedia.org/wiki/Thought_experimentshttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Computational_complexity_theoryhttp://en.wikipedia.org/wiki/Turing_machinehttp://en.wikipedia.org/wiki/Instruction_sethttp://en.wikipedia.org/wiki/Processor_registerhttp://en.wikipedia.org/wiki/Memory_hierarchyhttp://en.wikipedia.org/wiki/RAM_modelhttp://en.wikipedia.org/wiki/Random_accesshttp://en.wikipedia.org/wiki/Cache_memoryhttp://en.wikipedia.org/w/index.php?title=External-memory_model&action=edit&redlink=1http://en.wikipedia.org/wiki/Cache-oblivious_modelhttp://en.wikipedia.org/wiki/Microprocessorhttp://en.wikipedia.org/wiki/Interpreter_(computing)http://en.wikipedia.org/wiki/Virtual_machine


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as we mentioned before, many of the primality proving methods

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