The number 4003
4003 is a twin prime (4001 and 4003 are both prime) and the 552nd prime number. Its only divisors are 1 and 4003.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4003: a twin prime (4001 and 4003 are both prime); the 552nd prime number.
- 2
4003 is prime, so its only factors are 1 and 4003. It is the 552nd prime; the next prime is 4007 and the one before is 4001.
- 3
The divisors add up to 4004; without 4003 itself that is 1, so 4003 is deficient (1 is less than 4003). Euler's totient φ(4003) = 4002 numbers up to 4003 share no factor with it.
- 4
The digits of 4003 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 51 steps to reach 1.
4003 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 4004 |
| Euler totient φ(n) | 4002 |
| Square | 16024009 |
| Cube | 64144108027 |
| Square root | 63.269266 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 51 |
| Scientific notation | 4.003 × |
4003 in other forms
| Form | Value |
|---|---|
| In words | four thousand and three |
| Binary (base 2) | 111110100011 |
| Octal (base 8) | 7643 |
| Hexadecimal (base 16) | FA3 |
| Base 3 | 12111021 |
| As time | 4003 seconds = 1 h 6 min 43 s |
Is 4003 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 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | 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 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4003 a prime number?
Yes. 4003 is divisible only by 1 and itself.
What are the factors of 4003?
1, 4003.
What is 4003 in binary?
111110100011 (hexadecimal FA3, octal 7643).
What is the square root of 4003?
About 63.2693.
Is 4003 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 4003?
4003 is a twin prime (4001 and 4003 are both prime); the 552nd prime number.