sega at Sat, 13 Jul 2024 20:45:51 UTC No. 16280654

Primality of one
If the definition of a prime number were changed to call 1 a prime, many statements involving prime numbers would need to be reworded in a more awkward way. For example, the fundamental theorem of arithmetic would need to be rephrased in terms of factorizations into primes greater than 1, because every number would have multiple factorizations with any number of copies of 1.[40] Similarly, the sieve of Eratosthenes would not work correctly if it handled 1 as a prime, because it would eliminate all multiples of 1 (that is, all other numbers) and output only the single number 1.[42] Some other more technical properties of prime numbers also do not hold for the number 1: for instance, the formulas for Euler's totient function or for the sum of divisors function are different for prime numbers than they are for 1.[43] By the early 20th century, mathematicians began to agree that 1 should not be listed as prime, but rather in its own special category as a "unit".[40]

Anonymous at Sat, 13 Jul 2024 21:00:27 UTC No. 16280665

>>16280645
Because it's not. You retards get too worked up about semantics that has nothing to do with the math. You're not smart for pointing out
>"hurr 1 is also divisible by 1 and itself!!"
A prime is a specific set of numbers that meets a specific criteria and 1 simply isn't one of them.

Anonymous at Sat, 13 Jul 2024 21:06:19 UTC No. 16280670

Because it only has a single factor. Primes have 2.

Anonymous at Sat, 13 Jul 2024 21:22:38 UTC No. 16280681

>>16280665
>A prime is a specific set of numbers that meets a specific criteria and 1 simply isn't one of them.
Specific requirements which it meets retard "DURRR YOUR STUPID FOR ACTUALLY APPLYING THE CRITERIA ASKED FOR"""

Anonymous at Sat, 13 Jul 2024 21:30:21 UTC No. 16280685

>>16280645
>Are mathematicians retarded?
worse, they're autistic.

Anonymous at Sat, 13 Jul 2024 21:37:32 UTC No. 16280692

>>16280645
pluto is a planet

Anonymous at Sat, 13 Jul 2024 21:37:53 UTC No. 16280693

>>16280681
>Specific requirements which it meets
Then you're actually just retarded. Read >>16280670 for a simple reasoning to why it isn't. i.e. a prime is defined by properties 1 does not have. End of discussion.

Anonymous at Sat, 13 Jul 2024 21:38:28 UTC No. 16280695

>>16280692
Shut up shut up shut up

Anonymous at Sun, 14 Jul 2024 07:04:06 UTC No. 16281083

>>16280645
You're using a definition for which 1 IS a prime number (in mathematical logic, 'and' can be idempotent, so the 'and' in "1 and the number itself" doesn't imply distinctness between the two [natural] numbers).
That's not the definition that modern number theorists use, but it's completely fine to use your definition and include 1 as a prime number if it makes things more convenient for you in some contexts.
Like the endless posts on the Internet about order of operations and whatnot, conventions get elevated to a kind of objective status that they're not intended to have. They're just conventions so that people can understand one another and do interesting work.