What is the 2300th prime number?
The 2300th prime number is 20357. The next prime is 20359 (a gap of 2) and the one before is 20353.
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 2300th one is 20357.
- 2
20357 is prime because no prime up to ā20357 ā 142.68 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 2300th prime is close to 2300 Ć ln(2300) ā 17804, and here it is 20357.
- 4
20357 is a twin prime: 20357 and 20359 are both prime.
Primes around the 2300th
| Position | Prime | Gap from the previous |
|---|---|---|
| 2297 | 20341 | 8 |
| 2298 | 20347 | 6 |
| 2299 | 20353 | 6 |
| 2300 | 20357 | 4 |
| 2301 | 20359 | 2 |
| 2302 | 20369 | 10 |
| 2303 | 20389 | 20 |
Questions
What is the 2300th prime number?
20357.
Which prime number is 20357?
20357 is the 2300th prime number.
What is the sum of the first 2300 primes?
21,938,047.