The number 4001
4001 is a twin prime (4001 and 4003 are both prime) and the 551st prime number. Its only divisors are 1 and 4001.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4001: a twin prime (4001 and 4003 are both prime); the 551st prime number.
- 2
4001 is prime, so its only factors are 1 and 4001. It is the 551st prime; the next prime is 4003 and the one before is 3989.
- 3
The divisors add up to 4002; without 4001 itself that is 1, so 4001 is deficient (1 is less than 4001). Euler's totient φ(4001) = 4000 numbers up to 4001 share no factor with it.
- 4
The digits of 4001 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 43 steps to reach 1.
4001 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 4002 |
| Euler totient φ(n) | 4000 |
| Square | 16008001 |
| Cube | 64048012001 |
| Square root | 63.253458 |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 43 |
| Scientific notation | 4.001 × |
4001 in other forms
| Form | Value |
|---|---|
| In words | four thousand and one |
| Binary (base 2) | 111110100001 |
| Octal (base 8) | 7641 |
| Hexadecimal (base 16) | FA1 |
| Base 3 | 12111012 |
| As time | 4001 seconds = 1 h 6 min 41 s |
Is 4001 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 4) | 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 8) | 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 4001 a prime number?
Yes. 4001 is divisible only by 1 and itself.
What are the factors of 4001?
1, 4001.
What is 4001 in binary?
111110100001 (hexadecimal FA1, octal 7641).
What is the square root of 4001?
About 63.2535.
Is 4001 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 4001?
4001 is a twin prime (4001 and 4003 are both prime); the 551st prime number.