What is the 257th prime number?
The 257th prime number is 1621. The next prime is 1627 (a gap of 6) and the one before is 1619.
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 257th one is 1621.
- 2
1621 is prime because no prime up to ā1621 ā 40.26 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 257th prime is close to 257 Ć ln(257) ā 1426, and here it is 1621.
- 4
1621 is a twin prime: 1619 and 1621 are both prime.
Primes around the 257th
| Position | Prime | Gap from the previous |
|---|---|---|
| 254 | 1609 | 2 |
| 255 | 1613 | 4 |
| 256 | 1619 | 6 |
| 257 | 1621 | 2 |
| 258 | 1627 | 6 |
| 259 | 1637 | 10 |
| 260 | 1657 | 20 |
Questions
What is the 257th prime number?
1621.
Which prime number is 1621?
1621 is the 257th prime number.
What is the sum of the first 257 primes?
193,376.