What is the 4001st prime number?
The 4001st prime number is 37831. The next prime is 37847 (a gap of 16) and the one before is 37813.
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 4001st one is 37831.
- 2
37831 is prime because no prime up to ā37831 ā 194.50 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 4001st prime is close to 4001 Ć ln(4001) ā 33185, and here it is 37831.
- 4
37831 has no twin: neither 37829 nor 37833 is prime.
Primes around the 4001st
| Position | Prime | Gap from the previous |
|---|---|---|
| 3998 | 37799 | 16 |
| 3999 | 37811 | 12 |
| 4000 | 37813 | 2 |
| 4001 | 37831 | 18 |
| 4002 | 37847 | 16 |
| 4003 | 37853 | 6 |
| 4004 | 37861 | 8 |
Questions
What is the 4001st prime number?
37831.
Which prime number is 37831?
37831 is the 4001st prime number.
What is the sum of the first 4001 primes?
71,304,738.