The number 13001
13001 is a twin prime (13001 and 13003 are both prime) and the 1548th prime number. Its only divisors are 1 and 13001.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13001: a twin prime (13001 and 13003 are both prime); the 1548th prime number.
- 2
13001 is prime, so its only factors are 1 and 13001. It is the 1548th prime; the next prime is 13003 and the one before is 12983.
- 3
The divisors add up to 13002; without 13001 itself that is 1, so 13001 is deficient (1 is less than 13001). Euler's totient φ(13001) = 13000 numbers up to 13001 share no factor with it.
- 4
The digits of 13001 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
13001 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13002 |
| Euler totient φ(n) | 13000 |
| Square | 169026001 |
| Cube | 2197507039001 |
| Square root | 114.021928 |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 125 |
| Scientific notation | 1.3001 × |
13001 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand and one |
| Binary (base 2) | 11001011001001 |
| Octal (base 8) | 31311 |
| Hexadecimal (base 16) | 32C9 |
| Base 3 | 122211112 |
| As time | 13001 seconds = 3 h 36 min 41 s |
Is 13001 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 1) | 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 2) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13001 a prime number?
Yes. 13001 is divisible only by 1 and itself.
What are the factors of 13001?
1, 13001.
What is 13001 in binary?
11001011001001 (hexadecimal 32C9, octal 31311).
What is the square root of 13001?
About 114.0219.
Is 13001 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 13001?
13001 is a twin prime (13001 and 13003 are both prime); the 1548th prime number.