| Next prime | 4129 |
| Previous prime | 4111 |
| Octal | (10037)8 |
| Hexadecimal | (101F)16 |
| Prime gap | 2 |
| 108th Twin prime (the small number) | The big number is 4129 . |
| 73rd Prime triplet (the smallest number) | The others are 4129 and 4133 . |
| 210th Sexy prime (the small number) | The big number is 4133 . |
| 290th Prime of the Form 4n+3 | |
| 63rd Safe prime |