The number 13003
13003 is a twin prime (13001 and 13003 are both prime) and the 1549th prime number. Its only divisors are 1 and 13003.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13003: a twin prime (13001 and 13003 are both prime); the 1549th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13003 is prime, so its only factors are 1 and 13003. It is the 1549th prime; the next prime is 13007 and the one before is 13001.
- 3
The divisors add up to 13004; without 13003 itself that is 1, so 13003 is deficient (1 is less than 13003). Euler's totient φ(13003) = 13002 numbers up to 13003 share no factor with it.
- 4
The digits of 13003 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 125 steps to reach 1.
13003 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13004 |
| Euler totient φ(n) | 13002 |
| Square | 169078009 |
| Cube | 2198521351027 |
| Square root | 114.030698 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 125 |
| Scientific notation | 1.3003 × |
13003 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand and three |
| Binary (base 2) | 11001011001011 |
| Octal (base 8) | 31313 |
| Hexadecimal (base 16) | 32CB |
| Base 3 | 122211121 |
| As time | 13003 seconds = 3 h 36 min 43 s |
Is 13003 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 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 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 1) | 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 13003 a prime number?
Yes. 13003 is divisible only by 1 and itself.
What are the factors of 13003?
1, 13003.
What is 13003 in binary?
11001011001011 (hexadecimal 32CB, octal 31313).
What is the square root of 13003?
About 114.0307.
Is 13003 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 13003?
13003 is a twin prime (13001 and 13003 are both prime); the 1549th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.