Yes, 65,537 is a prime number. Its only factors are 1 and 65,537.
A number is prime if no smaller prime up to its square root divides it. The square root of 65,537 is about 256.00, 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, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241 and 251.
| Divide by | Remainder | Divides evenly? |
|---|---|---|
| 2 | 1 | No |
| 3 | 2 | No |
| 5 | 2 | No |
| 7 | 3 | No |
| 11 | 10 | No |
| 13 | 4 | No |
| 17 | 2 | No |
| 19 | 6 | No |
| 23 | 10 | No |
| 29 | 26 | No |
| 31 | 3 | No |
| 37 | 10 | No |
| 41 | 19 | No |
| 43 | 5 | No |
| 47 | 19 | No |
| 53 | 29 | No |
| 59 | 47 | No |
| 61 | 23 | No |
| 67 | 11 | No |
| 71 | 4 | No |
| 73 | 56 | No |
| 79 | 46 | No |
| 83 | 50 | No |
| 89 | 33 | No |
| 97 | 62 | No |
| 101 | 89 | No |
| 103 | 29 | No |
| 107 | 53 | No |
| 109 | 28 | No |
| 113 | 110 | No |
(First 30 of 54 tests shown; every remainder is non-zero.)
None of them divides 65,537 evenly, so 65,537 is prime.
| Number | Prime? |
|---|---|
| 5,003 | Yes |
| 7,919 | Yes |
| 9,973 | Yes |
| 10,007 | Yes |
Another number? Use the prime number checker for any value, or see the list of prime numbers.