181 is a prime number from 101-200. 181 has 2 factors, 1 and 181. It is the 42nd prime number, and the seventeenth prime number from 101-200.
Proofs[]
— 181 is divisible by 1.
— 181 is not divisible by 2-180.
- — 181 is divisible by 181.
Therefore, 181 is a prime number.
As an Exponent of Mersenne Number[]
2181 - 1 is divisible by 43,441, 1,164,193, 7,648,337, etc., and is therefore not a prime number.
Relationship with other odd numbers[]
The numbers before[]
- 173 is the second previous prime number.
- 175 is a composite number. Its prime factorization is 52 × 7.
- 177 is also a composite number. Its prime factorization is 3 × 59.
- 179 is the odd number and prime number preceding 181.
- The difference between 181 and 179 is 2. Therefore, they are twin primes.
The numbers after[]
- 183 is a composite number. Its prime factorization is 3 × 61.
- 185 is also a composite number. Its prime factorization is 5 × 37.
- 187 is another composite number. Its prime factorization is 11 × 17.
- 189 is yet another composite number. Its prime factorization is 33 × 7.
- 191 is the prime number following 181.
- 193 is the prime number following 191.
Trivia[]
- 181 is the difference between two consecutive perfect squares (912 - 902), as well as the sum of two consecutive squares (92 + 102).
- Since 181 is the sum of two consecutive squares, it is a centered square number.
- 181 is also a centered pentagonal number, a centered dodecagonal number, a centered 18-gonal number, and a centered 30-gonal number.
- Since 181 is the sum of two consecutive squares, it is a centered square number.
- 181 is an undulating number in base 10 as well as the 28th undulating prime.