What is the 856th prime number?
The 856th prime number is 6637. The next prime is 6653 (a gap of 16) and the one before is 6619.
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 856th one is 6637.
- 2
6637 is prime because no prime up to ā6637 ā 81.47 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 856th prime is close to 856 Ć ln(856) ā 5780, and here it is 6637.
- 4
6637 has no twin: neither 6635 nor 6639 is prime.
Primes around the 856th
| Position | Prime | Gap from the previous |
|---|---|---|
| 853 | 6599 | 18 |
| 854 | 6607 | 8 |
| 855 | 6619 | 12 |
| 856 | 6637 | 18 |
| 857 | 6653 | 16 |
| 858 | 6659 | 6 |
| 859 | 6661 | 2 |
Questions
What is the 856th prime number?
6637.
Which prime number is 6637?
6637 is the 856th prime number.
What is the sum of the first 856 primes?
2,635,161.