What is the 3997th prime number?
The 3997th prime number is 37783. The next prime is 37799 (a gap of 16) and the one before is 37781.
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 3997th one is 37783.
- 2
37783 is prime because no prime up to ā37783 ā 194.38 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3997th prime is close to 3997 Ć ln(3997) ā 33148, and here it is 37783.
- 4
37783 is a twin prime: 37781 and 37783 are both prime.
Primes around the 3997th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3994 | 37717 | 18 |
| 3995 | 37747 | 30 |
| 3996 | 37781 | 34 |
| 3997 | 37783 | 2 |
| 3998 | 37799 | 16 |
| 3999 | 37811 | 12 |
| 4000 | 37813 | 2 |
Questions
What is the 3997th prime number?
37783.
Which prime number is 37783?
37783 is the 3997th prime number.
What is the sum of the first 3997 primes?
71,153,484.