What is the 4002nd prime number?
The 4002nd prime number is 37847. The next prime is 37853 (a gap of 6) and the one before is 37831.
Position
Pick any whole number from 1 to 10,000.
How to work it out
- 1
List the primes in order: 2, 3, 5, 7, 11, 13, ā¦ The 4002nd one is 37847.
- 2
37847 is prime because no prime up to ā37847 ā 194.54 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 4002nd prime is close to 4002 Ć ln(4002) ā 33195, and here it is 37847.
- 4
37847 has no twin: neither 37845 nor 37849 is prime.
Primes around the 4002nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 3999 | 37811 | 12 |
| 4000 | 37813 | 2 |
| 4001 | 37831 | 18 |
| 4002 | 37847 | 16 |
| 4003 | 37853 | 6 |
| 4004 | 37861 | 8 |
| 4005 | 37871 | 10 |
Questions
What is the 4002nd prime number?
37847.
Which prime number is 37847?
37847 is the 4002nd prime number.
What is the sum of the first 4002 primes?
71,342,585.