The number 13931
13931 is a palindromic prime: it reads the same backwards and is prime, a twin prime (13931 and 13933 are both prime) and the 1647th prime number. Its only divisors are 1 and 13931.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13931: a palindromic prime: it reads the same backwards and is prime; a twin prime (13931 and 13933 are both prime); the 1647th prime number; a palindrome: it reads 13931 backwards too.
- 2
13931 is prime, so its only factors are 1 and 13931. It is the 1647th prime; the next prime is 13933 and the one before is 13921.
- 3
The divisors add up to 13932; without 13931 itself that is 1, so 13931 is deficient (1 is less than 13931). Euler's totient φ(13931) = 13930 numbers up to 13931 share no factor with it.
- 4
The digits of 13931 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 164 steps to reach 1.
13931 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13932 |
| Euler totient φ(n) | 13930 |
| Square | 194072761 |
| Cube | 2703627633491 |
| Square root | 118.029657 |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 164 |
| Scientific notation | 1.3931 × |
13931 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and thirty-one |
| Binary (base 2) | 11011001101011 |
| Octal (base 8) | 33153 |
| Hexadecimal (base 16) | 366B |
| Base 3 | 201002222 |
| As time | 13931 seconds = 3 h 52 min 11 s |
Is 13931 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | No (remainder 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13931 a prime number?
Yes. 13931 is divisible only by 1 and itself.
What are the factors of 13931?
1, 13931.
What is 13931 in binary?
11011001101011 (hexadecimal 366B, octal 33153).
What is the square root of 13931?
About 118.0297.
Is 13931 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 13931?
13931 is a palindromic prime: it reads the same backwards and is prime; a twin prime (13931 and 13933 are both prime); the 1647th prime number; a palindrome: it reads 13931 backwards too.