101 is the first 3-digit prime number. 101 has 2 factors, 1 and 101. It is the 26th prime number, and the first prime number from 101-200.
Proofs[]
— 101 is divisible by 1.
— 101 is not divisible by 2-100.
- — 101 is divisible by 101.
Therefore, 101 is a prime number.
As an Exponent of Mersenne Number[]
2101 - 1 is divisible by 7,432,339,208,719, and is therefore not a prime number.
Relationship with other odd numbers[]
The numbers before[]
- 89 is the previous prime number, preceding 97.
- 97 is the previous prime number.
- The difference between 101 and 97 is 4. Therefore, they are cousin primes.
- 99 is the previous odd number. It is a composite number; its prime factorization is 32 × 11.
The numbers after[]
- 103 is the next odd number, as well as the next prime number.
- The difference between 103 and 101 is 2. Therefore, they are twin primes.
- 105 is a composite number; its prime factorization is 3 × 5 × 7.
- 107 is the prime number following 103.
- The difference between 107 and 101 is 6. Therefore, they are sexy primes.
- 109 is the prime number following 107.
In science[]
- 101 is the atomic number of mendelevium.
- 101 is the Messier designation of the Pinwheel Galaxy located in Ursa Major.
In books[]
- 101 is often used in titles of books that contain a list of items, such as 101 of the Best.... This is a marketing scheme that implies the reader will get a little bit of extra information compared to books that only list 100 items.
Trivia[]
- 101 is a twin prime, cousin prime, and sexy prime, all at once.
- 101 is the only known prime number of the form 10n + 1.
- 101 is the first 3-digit palindromic prime.
- 101 is the only existing prime number with alternating 1s and 0s in its decimal expansion.
- 101 is both a dihedral prime and a strobogrammatic prime.
- 101 is the smallest number that can be expressed as the sum of three distinct nonzero squares in more than two ways.