What is the 4000th prime number?
The 4000th prime number is 37813. The next prime is 37831 (a gap of 18) and the one before is 37811.
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 4000th one is 37813.
- 2
37813 is prime because no prime up to ā37813 ā 194.46 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 4000th prime is close to 4000 Ć ln(4000) ā 33176, and here it is 37813.
- 4
37813 is a twin prime: 37811 and 37813 are both prime.
Primes around the 4000th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3997 | 37783 | 2 |
| 3998 | 37799 | 16 |
| 3999 | 37811 | 12 |
| 4000 | 37813 | 2 |
| 4001 | 37831 | 18 |
| 4002 | 37847 | 16 |
| 4003 | 37853 | 6 |
Questions
What is the 4000th prime number?
37813.
Which prime number is 37813?
37813 is the 4000th prime number.
What is the sum of the first 4000 primes?
71,266,907.