Yes, 9,973 is a prime number. Its only factors are 1 and 9,973.
A number is prime if no smaller prime up to its square root divides it. The square root of 9,973 is about 99.86, so it is enough to test the primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.
| Divide by | Remainder | Divides evenly? |
|---|---|---|
| 2 | 1 | No |
| 3 | 1 | No |
| 5 | 3 | No |
| 7 | 5 | No |
| 11 | 7 | No |
| 13 | 2 | No |
| 17 | 11 | No |
| 19 | 17 | No |
| 23 | 14 | No |
| 29 | 26 | No |
| 31 | 22 | No |
| 37 | 20 | No |
| 41 | 10 | No |
| 43 | 40 | No |
| 47 | 9 | No |
| 53 | 9 | No |
| 59 | 2 | No |
| 61 | 30 | No |
| 67 | 57 | No |
| 71 | 33 | No |
| 73 | 45 | No |
| 79 | 19 | No |
| 83 | 13 | No |
| 89 | 5 | No |
| 97 | 79 | No |
None of them divides 9,973 evenly, so 9,973 is prime.
| Number | Prime? |
|---|---|
| 3,001 | Yes |
| 4,001 | Yes |
| 5,003 | Yes |
| 7,919 | Yes |
| 10,007 | Yes |
| 65,537 | Yes |
Another number? Use the prime number checker for any value, or see the list of prime numbers.