The number 521
521 is a twin prime (521 and 523 are both prime) and the 98th prime number. Its only divisors are 1 and 521.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 521: a twin prime (521 and 523 are both prime); the 98th prime number.
- 2
521 is prime, so its only factors are 1 and 521. It is the 98th prime; the next prime is 523 and the one before is 509.
- 3
The divisors add up to 522; without 521 itself that is 1, so 521 is deficient (1 is less than 521). Euler's totient φ(521) = 520 numbers up to 521 share no factor with it.
- 4
The digits of 521 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 123 steps to reach 1.
521 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 522 |
| Euler totient φ(n) | 520 |
| Square | 271441 |
| Cube | 141420761 |
| Square root | 22.825424 |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 123 |
| Scientific notation | 5.21 × |
521 in other forms
| Form | Value |
|---|---|
| In words | five hundred and twenty-one |
| Roman numerals | DXXI |
| Binary (base 2) | 1000001001 |
| Octal (base 8) | 1011 |
| Hexadecimal (base 16) | 209 |
| Base 3 | 201022 |
| As time | 521 seconds = 8 min 41 s |
Is 521 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 3) | 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 8) | 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 4) | 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 521 a prime number?
Yes. 521 is divisible only by 1 and itself.
What are the factors of 521?
1, 521.
What is 521 in binary?
1000001001 (hexadecimal 209, octal 1011).
What is the square root of 521?
About 22.8254.
What is 521 in Roman numerals?
DXXI.
Is 521 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 521?
521 is a twin prime (521 and 523 are both prime); the 98th prime number.