What is the 820th prime number?
The 820th prime number is 6301. The next prime is 6311 (a gap of 10) and the one before is 6299.
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 820th one is 6301.
- 2
6301 is prime because no prime up to ā6301 ā 79.38 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 820th prime is close to 820 Ć ln(820) ā 5502, and here it is 6301.
- 4
6301 is a twin prime: 6299 and 6301 are both prime.
Primes around the 820th
| Position | Prime | Gap from the previous |
|---|---|---|
| 817 | 6277 | 6 |
| 818 | 6287 | 10 |
| 819 | 6299 | 12 |
| 820 | 6301 | 2 |
| 821 | 6311 | 10 |
| 822 | 6317 | 6 |
| 823 | 6323 | 6 |
Questions
What is the 820th prime number?
6301.
Which prime number is 6301?
6301 is the 820th prime number.
What is the sum of the first 820 primes?
2,402,537.