137 is a 3-digit prime number. 137 has 2 factors, 1 and 137. It is the 33rd prime number, and the eighth prime number from 101-200.
Proofs[]
— 137 is divisible by 1.
— 137 is not divisible by 2-136.
- — 137 is divisible by 137.
As an Exponent of Mersenne Number[]
2137 - 1 is not a prime number. It is divisible by 32,032,215,596,496,435,569.
Relationship with other odd numbers[]
The numbers before[]
- 127 is the second previous prime number.
- 129 is a composite number; its prime factorization is 3 × 43.
- 131 is the prime number preceding 137.
- The difference between 137 and 131 is 6. Therefore, they are sexy primes.
- 133 is a composite number; its prime factorization is 7 × 19.
- 135 is a composite number; its prime factorization is 33 × 5.
The numbers after[]
- 139 is the next odd number, as well as the next prime number.
- The difference between 139 and 137 is 2. Therefore, they are twin primes.
- 141 is a composite number; its prime factorization is 3 × 47.
- 143 is also a composite number; its prime factorization is 11 × 13.
- 145 is yet another composite number; its prime factorization is 5 × 29.
- 147 is unsurprisingly a composite number; its prime factorization is 3 × 72.
- 149 is the prime number following 139.
Trivia[]
- Since 137 is the smaller component of the twin prime pair (137, 139), it is a Chen prime.
- 137 is a Pythagorean prime, since it is of the form 4n + 1. In this case, n = 34.
- 137 is a strong prime, since it is greater than the arithmetic mean of its prime neighbors.
- 137 is the integer part of the value of the golden angle, which is equal to 137.507764050037854646...
- 137 = 5! + 4! - 3! - 2! + 1! = 120 + 24 - 6 - 2 + 1
- 137 is a factor of 10,001 and the repunit 11,111,111.
- In decimal notation, the value of is 0.00729927. Its period value is palindromic (excluding the zeros) and has a length of 8. However, this is only special to base 10.
