e-book The Prime Numbers (Advance Level) Practical; Volume 10: Mathematics for Beginners

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A prime number (or a prime) is a natural number greater than 1 that cannot be formed by .. Primes can thus be considered the "basic building blocks" of the natural numbers . Also, any even integer greater than 10 can be written as the sum of six primes. Dyslexia, Dyscalculia and Mathematics: A practical guide (​2nd ed.).
Table of contents

Evil integers but see also. Odious numbers. Primitive odious numbers. Pernicious numbers. Narcissistic Armstrong Plus perfect numbers. Powers of 2. Perfect powers without duplications. Perfect powers with duplications. Perfect squares.

Perfect cubes. Taxicab numbers Ta n ; only six are known. Abundant numbers. Primitive abundant numbers. Composite numbers. Deficient numbers. Perfect numbers.

Chapter 2: The quick tests for small numbers and probable primes

Practical numbers. Squarefree numbers. Not divisible by any perfect square. Untouchable numbers. Weird numbers.


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Amicable number pairs n,m. Aspiring numbers. Lehmer five numbers. First five n whose As n might be totally a-periodic. Sequences related to prime numbers and prime factorizations. Achilles numbers. Euler 's pseudoprimes in base 2. Powerful numbers also squareful or 2-full. Prime twins starting element. Prime cousins starting element. Prime triples starting element. Prime quadruples starting element. Primorial numbers prime n.

Pseudoprimes to base 2 Sarrus numbers.

Pseudoprimes to base 3. Semiprimes also biprimes. Pierpont primes. Thabit primes so far, 62 are known. Wieferich primes. Wilson primes. Wolstenholme primes.

The Mathematical Magic of the Fibonacci Numbers

Sequences related to partitions and compositions. Polite numbers staircase numbers. Politeness of a number. Baum - Sweet sequence. Fredholm-Rueppel sequence. Fibonacci words ; binary:. Infinite Fibonacci word. Rabbit sequence ; binary click here for dec :. Rabbit number ; binary:. Converted to decimal, gives the rabbit constant. Golay - Rudin - Shapiro sequence. Thue - Morse sequence t n. Combinatorial numbers such as Pascal - Tartaglia triangle binomials, Stirling, Lah and Franel numbers.

Euler zig-zag numbers A n. Franel numbers of order 3. Stirling numbers of the second kind S n,m ; number of partitions of n distinct elements into m non-empty subsets.

Prime and composite numbers intro (article) | Khan Academy

Counting enumeration sequences relevant to finite sets. Enumerations of set-related objects, assuming labeled elements. Subsets cardinality of the power set. Derangements subfactorials! Operators, mappings functions of a set into itself. Binary relations Digraphs with self-loops. Reflexive relations Irreflexive relations. Symmetric relations. Transitive relations. Preorder relations quasi-orderings. Partial-order relations posets. Total-preorder rels Weakly ordered partitions.

Ordered Bell numbers , or Fubini numbers.

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Total-order relations Bijections. Also permutations orders of symmetry groups S n. Equivalence relations Set partitions. Bell numbers B n. Abelian groupoids. Commutative CBOs. Non-associative Abelian groupoids. Commutative but non-associative CBOs. Non-associative non-Abelian groupoids. Associative CBOs. Non-Abelian semigroups. Associative but non-commutative CBOs. Abelian semigroups. Associative and commutative CBOs. Associative CBOs with an identity element. Non-Abelian monoids. Associative but non-commutative CBOs with identity.

Abelian monoids.

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Associative CBOs with identity and invertible elements. Abelian groups commutative. Non-Abelian groups. The following items in this section count the isomorphism classes of the specified objects on n labeled nodes.