What is the 3996th prime number?
The 3996th prime number is 37781. The next prime is 37783 (a gap of 2) and the one before is 37747.
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 3996th one is 37781.
- 2
37781 is prime because no prime up to ā37781 ā 194.37 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3996th prime is close to 3996 Ć ln(3996) ā 33139, and here it is 37781.
- 4
37781 is a twin prime: 37781 and 37783 are both prime.
Primes around the 3996th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3993 | 37699 | 6 |
| 3994 | 37717 | 18 |
| 3995 | 37747 | 30 |
| 3996 | 37781 | 34 |
| 3997 | 37783 | 2 |
| 3998 | 37799 | 16 |
| 3999 | 37811 | 12 |
Questions
What is the 3996th prime number?
37781.
Which prime number is 37781?
37781 is the 3996th prime number.
What is the sum of the first 3996 primes?
71,115,701.