- ☀️Daily Log:
- #til2022 Carmichael Numbers
- 🌐: https://www.quantamagazine.org/teenager-solves-stubborn-riddle-about-prime-number-look-alikes-20221013/
- 💁♂️: They are prime-lookalikes that passes Pierre de Fermat’s “little theorem” inspired prime test
- Little theorem - “if N is a prime number, then $$b^N -b$$ is always a multiple of N”
- Prime test - the reverse of Little theorem be a test for prime, that by checking $$b^N -b$$ is a multiple of N for all values of b, then N must be prime
- The composite numbers that breaks this prime test is known as Carmichael Numbers and the smallest of such numbers is 561
- More concretely, the Carmichael Numbers are defined by Korselt’s criterion
- 🤔: It was proven that there are also infinite amount of these numbers but mathematicians have no idea how they are distributed
- A 17 year old teenager named Daniel Larsen showed a proof to determine if a gap will contain a Carmichael number that was not limited to very large numbers
- https://arxiv.org/abs/2111.06963v1
- Retrospective::