What is the 900th prime number?
The 900th prime number is 6997. The next prime is 7001 (a gap of 4) and the one before is 6991.
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 900th one is 6997.
- 2
6997 is prime because no prime up to ā6997 ā 83.65 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 900th prime is close to 900 Ć ln(900) ā 6122, and here it is 6997.
- 4
6997 has no twin: neither 6995 nor 6999 is prime.
Primes around the 900th
| Position | Prime | Gap from the previous |
|---|---|---|
| 897 | 6977 | 6 |
| 898 | 6983 | 6 |
| 899 | 6991 | 8 |
| 900 | 6997 | 6 |
| 901 | 7001 | 4 |
| 902 | 7013 | 12 |
| 903 | 7019 | 6 |
Questions
What is the 900th prime number?
6997.
Which prime number is 6997?
6997 is the 900th prime number.
What is the sum of the first 900 primes?
2,935,471.