Prime number

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A prime number[1] is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number[2].

Prime numbers come into play in a number of ways in the Game of Life and OCA. Here are some of them:

  • Large prime oscillators whose periods are very large prime numbers, right up to the largest known prime number
  • Primer, a pattern that produces a stream of lightweight spaceships representing prime numbers
  • Prime calculators using guns whose output stream is filtered by primer to generate twin primes, prime quadruplets, cousin primes, and so forth
  • Fermat prime calculator, a pattern based on primer that calculates Fermat prime numbers
  • Izhora, the largest known cellular automation computer, which can be used to calculate prime numbers

Classes of prime numbers

A Mersenne prime[3] is a prime number that is one less than a power of two.

A Fermat prime[4] is a prime number of the form 2^(2^n)+1, where n is a nonnegative integer. Only five Fermat primes are known, namely 3, 5, 17, 257, and 65537.

A twin prime[5] is a prime number that is either 2 less or 2 more than another prime number — for example, either member of the twin prime pair (41, 43).

Medium-period prime-period oscillators

There are very few known prime-period oscillators above 16, although more are starting to be found with symmetric CatForce. Alternative[which?] forms of the same oscillator are combined into one.

References

  1. Prime number at Wikipedia
  2. Composite number at Wikipedia
  3. Mersenne prime at Wikipedia
  4. Fermat prime at Wikipedia
  5. Twin prime at Wikipedia
  6. Carson Cheng (Aug 05, 2022). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  7. Mitchell Riley (Aug 02, 2022). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  8. Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  9. Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums