What is the 2256th prime number?
The 2256th prime number is 19961. The next prime is 19963 (a gap of 2) and the one before is 19949.
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 2256th one is 19961.
- 2
19961 is prime because no prime up to ā19961 ā 141.28 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 2256th prime is close to 2256 Ć ln(2256) ā 17419, and here it is 19961.
- 4
19961 is a twin prime: 19961 and 19963 are both prime.
Primes around the 2256th
| Position | Prime | Gap from the previous |
|---|---|---|
| 2253 | 19927 | 8 |
| 2254 | 19937 | 10 |
| 2255 | 19949 | 12 |
| 2256 | 19961 | 12 |
| 2257 | 19963 | 2 |
| 2258 | 19973 | 10 |
| 2259 | 19979 | 6 |
Questions
What is the 2256th prime number?
19961.
Which prime number is 19961?
19961 is the 2256th prime number.
What is the sum of the first 2256 primes?
21,051,295.