What is the 857th prime number?
The 857th prime number is 6653. The next prime is 6659 (a gap of 6) and the one before is 6637.
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 857th one is 6653.
- 2
6653 is prime because no prime up to ā6653 ā 81.57 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 857th prime is close to 857 Ć ln(857) ā 5788, and here it is 6653.
- 4
6653 has no twin: neither 6651 nor 6655 is prime.
Primes around the 857th
| Position | Prime | Gap from the previous |
|---|---|---|
| 854 | 6607 | 8 |
| 855 | 6619 | 12 |
| 856 | 6637 | 18 |
| 857 | 6653 | 16 |
| 858 | 6659 | 6 |
| 859 | 6661 | 2 |
| 860 | 6673 | 12 |
Questions
What is the 857th prime number?
6653.
Which prime number is 6653?
6653 is the 857th prime number.
What is the sum of the first 857 primes?
2,641,814.