prime number

Examples of prime number in the following topics:

• Factors

  • Prime factorization is a particular type of factorization that breaks a number of interest into prime numbers that when multiplied back together produce the original number.
  • Such prime numbers are called prime factors.
  • Also note that 2 and 3 are prime numbers, because each is divisible by only 1 and itself.
  • We have now found factors for 12 that are all prime numbers.
  • This process repeats for each subsequent factor of the original number until all the factors at the bottoms of the branches are prime.

• Rational Algebraic Expressions

  • For each of the denominators, we find all the prime factors, the prime numbers that multiply to give that number.
  • If you are not familiar with the concept of prime factors, it may take a few minutes to get used to. $2\cdot 2 \cdot 3$ is 12 broken into its prime factors: that is, it is the list of prime numbers that multiply to give 12.
  • Similarly, the prime factors of 30 are 2, 3, and 5.
  • Because $12=2 \cdot 2 \cdot 3$, any number whose prime factors include two 2's and one 3 will be a multiple of 12.
  • Similarly, any number whose prime factors include a 2, a 3, and a 5 will be a multiple of 30.

• Common Bases of Logarithms

  • They describe musical intervals, appear in formulas counting prime numbers, inform some models in psychophysics, and can aid in forensic accounting.
  • The safety index, because it is a logarithm, is a much smaller number.
  • Clearly, $7$ is an easier number for our brain to handle.
  • Natural logarithms are closely linked to counting prime numbers ($2, 3, 5, 7$ ...), an important topic in number theory.
  • The prime number theorem states that for large enough N, the probability that a random integer not greater than N is prime is very close to $\frac {1} {log(N)}$.

• Introduction to Factoring Polynomials

  • The aim of factoring is to reduce objects to "basic building blocks", such as integers to prime numbers, or polynomials to irreducible polynomials.

• Introduction to Sequences

  • A mathematical sequence is an ordered list of objects, often numbers.
  • Sometimes the numbers in a sequence are defined in terms of a previous number in the list.
  • For example, the sequence of prime numbers $(2,3,5,7,11, \cdots )$ is the function $1→2, 2→3, 3→5, 4→7, 5→11, \cdots$ .
  • A geometric sequence is a list where each number is generated by multiplying a constant by the previous number.
  • Part of an infinite sequence of real numbers (in blue).

• Inverses of Composite Functions

• Introduction to Complex Numbers

  • A complex number has the form $a+bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit.
  • A complex number is a number that can be put in the form $a+bi$ where $a$ and $b$ are real numbers and $i$ is called the imaginary unit, where $i^2=-1$.
  • A complex number whose real part is zero is said to be purely imaginary, whereas a complex number whose imaginary part is zero is a real number.
  • It is beneficial to think of the set of complex numbers as an extension of the set of real numbers.
  • Complex numbers allow for solutions to certain equations that have no real number solutions.

• Roots of Complex Numbers

• Trigonometry and Complex Numbers: De Moivre's Theorem

• Exponential Decay

  • The exponential decay of the substance is a time-dependent decline and a prime example of exponential decay.