A prime number is a number p that is a divisor of some numbers but not others, such that for any possible a × b that is divisible by p, either a or b is also divisible by p. For example, −47 is a prime number since, for example, 37 × 94 is divisible by −47, and we see that 94 is also divisible by −47. Compare to the fact that 48 is not a prime number, as we can readily find, for example, that 3 × 32 is divisible by 48, but neither 3 nor 32 is divisible by 48.
In elementary number theory, as appears in movies and TV shows, a much weaker definition of prime number can be used, such as one limiting consideration to positive integers, in that a prime number is a positive integer that is divisible only by 1 and itself. In the example, 47 is divisible by 1 and 47 but not any other integer in between, while 48 is divisible by 1 and 48 as well as 2, 3, 4, 6, 8, ..., 24.
Prime numbers are an important part of First-Contact Math. The number 1 is not considered prime any more by human mathematicians, as it lacks certain important qualities of prime numbers (for one thing, and perhaps most importantly, 1 is a divisor of every other integer). But if the aliens include it in their listing of prime numbers, it still demonstrates their intelligence, as the sequence is unlikely to be the result of random blips.
A tenuous argument could be made that 0 is a prime number, but since that would correspond to zero blips, it's unlikely the extraterrestrials would list it.
In Sloane's On-Line Encyclopedia of Integer Sequences (OEIS), the prime numbers are listed at entry A40
. The very similar entry A8578 starts with 1 and entry A158611 starts with 0 and 1.
References in media:
Anime & Manga
- Jo Jos Bizarre Adventure Stone Ocean: In stressful situations, the Big Bad Enrico Pucci counts prime numbers to calm down, believing their indivisibility gives him strength and security. He has made a couple slip-ups before correcting himself, counting "28" by mistake.
Literature
- The Curious Incident of the Dog in the Night-time: This novel uses prime numbers for it's chapters instead of the standard numerical order, because the narrator likes prime numbers.
Live-Action TV
- Young Sheldon: In 'Demons, Sunday School, and Prime Numbers', Sheldon invents his own religion, mathology, the worship of integers. "Welcome to the Church of Mathology," Sheldon says to Billy, the only other person who came to the service in Sheldon's garage. "Today, I'd like to talk about prime numbers, and why they bring us joy." Billy says "Hallelujah" and the episode ends without actually elaborating anything about prime numbers. The numbers 0 and 1, neither of which is generally thought of as prime, figure much more prominently in the episode.
- Monk: In "Mr. Monk Gets Lotto Fever", a "lottery fanatic" (Malcolm Barrett) expresses amazement that three prime numbers would come up in the lottery drawing before a "lottery girl" was killed. However, considering that twenty-five of the first one hundred positive integers are primes, this would seem to be a case of Guy's law of small numbers.
Video Games
- Pokémon: The Ultra Beasts, as well as their honorary members, the Cosmog evolutionary family and Necrozma, are a group of extradimensional Pokémon who all share a prime number motif. Their base stats all being prime numbers, as well as the levels they learned new moves during Generation VII, and in the Cosmog line's case, levels that cause evolution.Exceptions
