What is the 3900th prime number?
The 3900th prime number is 36781. The next prime is 36787 (a gap of 6) and the one before is 36779.
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 3900th one is 36781.
- 2
36781 is prime because no prime up to ā36781 ā 191.78 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3900th prime is close to 3900 Ć ln(3900) ā 32248, and here it is 36781.
- 4
36781 is a twin prime: 36779 and 36781 are both prime.
Primes around the 3900th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3897 | 36761 | 12 |
| 3898 | 36767 | 6 |
| 3899 | 36779 | 12 |
| 3900 | 36781 | 2 |
| 3901 | 36787 | 6 |
| 3902 | 36791 | 4 |
| 3903 | 36793 | 2 |
Questions
What is the 3900th prime number?
36781.
Which prime number is 36781?
36781 is the 3900th prime number.
What is the sum of the first 3900 primes?
67,538,035.