What is the 256th prime number?
The 256th prime number is 1619. The next prime is 1621 (a gap of 2) and the one before is 1613.
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 256th one is 1619.
- 2
1619 is prime because no prime up to ā1619 ā 40.24 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 256th prime is close to 256 Ć ln(256) ā 1420, and here it is 1619.
- 4
1619 is a twin prime: 1619 and 1621 are both prime.
Primes around the 256th
| Position | Prime | Gap from the previous |
|---|---|---|
| 253 | 1607 | 6 |
| 254 | 1609 | 2 |
| 255 | 1613 | 4 |
| 256 | 1619 | 6 |
| 257 | 1621 | 2 |
| 258 | 1627 | 6 |
| 259 | 1637 | 10 |
Questions
What is the 256th prime number?
1619.
Which prime number is 1619?
1619 is the 256th prime number.
What is the sum of the first 256 primes?
191,755.