The number 10009
10009 is a twin prime (10007 and 10009 are both prime) and the 1231st prime number. Its only divisors are 1 and 10009.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10009: a twin prime (10007 and 10009 are both prime); the 1231st prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
10009 is prime, so its only factors are 1 and 10009. It is the 1231st prime; the next prime is 10037 and the one before is 10007.
- 3
The divisors add up to 10010; without 10009 itself that is 1, so 10009 is deficient (1 is less than 10009). Euler's totient φ(10009) = 10008 numbers up to 10009 share no factor with it.
- 4
The digits of 10009 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 166 steps to reach 1.
10009 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 10010 |
| Euler totient φ(n) | 10008 |
| Square | 100180081 |
| Cube | 1002702430729 |
| Square root | 100.044990 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 166 |
| Scientific notation | 1.0009 × |
10009 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and nine |
| Binary (base 2) | 10011100011001 |
| Octal (base 8) | 23431 |
| Hexadecimal (base 16) | 2719 |
| Base 3 | 111201201 |
| As time | 10009 seconds = 2 h 46 min 49 s |
Is 10009 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 1) | 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 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | 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 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10009 a prime number?
Yes. 10009 is divisible only by 1 and itself.
What are the factors of 10009?
1, 10009.
What is 10009 in binary?
10011100011001 (hexadecimal 2719, octal 23431).
What is the square root of 10009?
About 100.0450.
Is 10009 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 10009?
10009 is a twin prime (10007 and 10009 are both prime); the 1231st prime number; a happy number: repeatedly adding the squares of its digits reaches 1.