The number 10093
10093 is a twin prime (10091 and 10093 are both prime) and the 1239th prime number. Its only divisors are 1 and 10093.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10093: a twin prime (10091 and 10093 are both prime); the 1239th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
10093 is prime, so its only factors are 1 and 10093. It is the 1239th prime; the next prime is 10099 and the one before is 10091.
- 3
The divisors add up to 10094; without 10093 itself that is 1, so 10093 is deficient (1 is less than 10093). Euler's totient φ(10093) = 10092 numbers up to 10093 share no factor with it.
- 4
The digits of 10093 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 135 steps to reach 1.
10093 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 10094 |
| Euler totient φ(n) | 10092 |
| Square | 101868649 |
| Cube | 1028160274357 |
| Square root | 100.463924 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 135 |
| Scientific notation | 1.0093 × |
10093 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and ninety-three |
| Binary (base 2) | 10011101101101 |
| Octal (base 8) | 23555 |
| Hexadecimal (base 16) | 276D |
| Base 3 | 111211211 |
| As time | 10093 seconds = 2 h 48 min 13 s |
Is 10093 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 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 6) | 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 10093 a prime number?
Yes. 10093 is divisible only by 1 and itself.
What are the factors of 10093?
1, 10093.
What is 10093 in binary?
10011101101101 (hexadecimal 276D, octal 23555).
What is the square root of 10093?
About 100.4639.
Is 10093 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 10093?
10093 is a twin prime (10091 and 10093 are both prime); the 1239th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.