What is the 2257th prime number?
The 2257th prime number is 19963. The next prime is 19973 (a gap of 10) and the one before is 19961.
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 2257th one is 19963.
- 2
19963 is prime because no prime up to ā19963 ā 141.29 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 2257th prime is close to 2257 Ć ln(2257) ā 17428, and here it is 19963.
- 4
19963 is a twin prime: 19961 and 19963 are both prime.
Primes around the 2257th
| Position | Prime | Gap from the previous |
|---|---|---|
| 2254 | 19937 | 10 |
| 2255 | 19949 | 12 |
| 2256 | 19961 | 12 |
| 2257 | 19963 | 2 |
| 2258 | 19973 | 10 |
| 2259 | 19979 | 6 |
| 2260 | 19991 | 12 |
Questions
What is the 2257th prime number?
19963.
Which prime number is 19963?
19963 is the 2257th prime number.
What is the sum of the first 2257 primes?
21,071,258.