What is the 3993rd prime number?
The 3993rd prime number is 37699. The next prime is 37717 (a gap of 18) and the one before is 37693.
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 3993rd one is 37699.
- 2
37699 is prime because no prime up to ā37699 ā 194.16 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3993rd prime is close to 3993 Ć ln(3993) ā 33111, and here it is 37699.
- 4
37699 has no twin: neither 37697 nor 37701 is prime.
Primes around the 3993rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 3990 | 37663 | 6 |
| 3991 | 37691 | 28 |
| 3992 | 37693 | 2 |
| 3993 | 37699 | 6 |
| 3994 | 37717 | 18 |
| 3995 | 37747 | 30 |
| 3996 | 37781 | 34 |
Questions
What is the 3993rd prime number?
37699.
Which prime number is 37699?
37699 is the 3993rd prime number.
What is the sum of the first 3993 primes?
71,002,456.