Yes, 521 is a prime number. Its only factors are 1 and 521.
A number is prime if no smaller prime up to its square root divides it. The square root of 521 is about 22.83, so it is enough to test the primes 2, 3, 5, 7, 11, 13, 17 and 19.
| Divide by | Remainder | Divides evenly? |
|---|---|---|
| 2 | 1 | No |
| 3 | 2 | No |
| 5 | 1 | No |
| 7 | 3 | No |
| 11 | 4 | No |
| 13 | 1 | No |
| 17 | 11 | No |
| 19 | 8 | No |
None of them divides 521 evenly, so 521 is prime.
| Number | Prime? |
|---|---|
| 499 | Yes |
| 500 | No, 2 × 2 × 5 × 5 × 5 |
| 501 | No, 3 × 167 |
| 511 | No, 7 × 73 |
| 539 | No, 7 × 7 × 11 |
| 541 | Yes |
| 561 | No, 3 × 11 × 17 |
| 601 | Yes |
Another number? Use the prime number checker for any value, or see the list of prime numbers.