Yes, 1,601 is a prime number. Its only factors are 1 and 1,601.
A number is prime if no smaller prime up to its square root divides it. The square root of 1,601 is about 40.01, so it is enough to test the primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 and 37.
| Divide by | Remainder | Divides evenly? |
|---|---|---|
| 2 | 1 | No |
| 3 | 2 | No |
| 5 | 1 | No |
| 7 | 5 | No |
| 11 | 6 | No |
| 13 | 2 | No |
| 17 | 3 | No |
| 19 | 5 | No |
| 23 | 14 | No |
| 29 | 6 | No |
| 31 | 20 | No |
| 37 | 10 | No |
None of them divides 1,601 evenly, so 1,601 is prime.
| Number | Prime? |
|---|---|
| 1,297 | Yes |
| 1,357 | No, 23 × 59 |
| 1,459 | Yes |
| 1,501 | No, 19 × 79 |
| 1,729 | No, 7 × 13 × 19 |
| 1,801 | Yes |
| 1,901 | Yes |
| 1,999 | Yes |
Another number? Use the prime number checker for any value, or see the list of prime numbers.