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.

• Entailment Discussion for 4th Grade Operations

  • Entailments discussion prompts to refine and adapt your realization of operations on elementary number sets:
  • What makes a number prime?
  • Is one a prime number?
  • Is that relationship still true regardless of what number sets these operations are operating on?
  • Are there specific numbers where the operations are easily to calculate with?

• 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.

• Complementary Events

  • If you were asked to choose any number, you might think that that number could either be prime or composite.
  • Clearly, a number cannot be both prime and composite, so that takes care of the mutually exclusive property.
  • However, being prime or being composite are not exhaustive because the number 1 in mathematics is designated as "unique. "

• Set Class and Prime Form (2)

  • Set classes that have the same number of notes in them (we say that they have the same "cardinality") are grouped together: trichords (three-note pitch-class sets) sit together, as do nonachords (nine-note pitch-class sets), and so on.
  • Prime form for each set class is show in parenthesis.
  • The "Forte Number" (3-1, 9-1, etc.), often adjacent to the prime form, was given to each set class by the famous music theorist [Allen Forte][4], who was one of the first to describe the set class list.
  • The interval class vector next to each set class's prime form is particularly valuable.

• Melodic Keyboard-Style Voice-Leading

  • In order to avoid confusion with rhythmic numbers, trinket uses a version of the Helmholtz register designation.
  • ISO Octave 6 takes two primes (c'), Octave 7 three primes (c'), etc.
  • Rhythms are designated by numbers representing note values—2 for half note, 4 for quarter note, etc.
  • These numbers immediately follow the pitches.

• Unconscious Perception

  • This is one of the simplest examples of priming.
  • One example of priming is in the childhood game Simon Says.
  • Simon is able to trick the players because of priming.
  • The participants who had been primed with rude words interrupted the investigator most often, and those primed with polite words did so the least often.
  • A number of studies have examined how unconscious stimuli influence human perception.

• Analyzing 12-tone music

  • Any row form that is the same as, or a strict transposition of, that opening prime form is also a prime form.
  • Once you have labeled the main prime form at the beginning of the piece, any subsequent row that is an exact transposition of that row is prime.
  • There are multiple common systems for deciding the numbering.
  • The simplest, which we will follow in this course, is to number the row by its starting pitch class.
  • If the prime form begins on G (7), it is P7; on B (11), P11.

• [PF content: The Prime Minister]

• Naming Intervals

  • This gives you the number for the interval.