Exploring the Number 149
149 (one hundred and forty-nine) is the natural number that lies between 148 and 150.
In Mathematics
The number 149 holds special significance as it is the 35th prime number. It is notable for being the first prime number with a difference of exactly 10 from the preceding prime number. Additionally, it is classified as an emirp and an irregular prime.
After 1 and 127, it is recognized as the third smallest de Polignac number, which is an odd number that cannot be expressed as a prime number plus a power of two. More specifically, following 1, it is the second smallest number that cannot be represented as a sum of two prime powers.
Moreover, 149 is categorized as a Tribonacci number, as it can be calculated by the sum of the three preceding numbers: 24, 44, and 81.
Interesting Facts
- There are exactly 149 integer points in a closed circular disk with a radius of 7.
- It is also noted that there are exactly 149 ways to position six queens on a 5 × 5 chess board, ensuring that each queen attacks exactly one other queen.
- Furthermore, the barycentric subdivision of a tetrahedron gives rise to an abstract simplicial complex that comprises exactly 149 simplices.