What is the 254th prime number?
The 254th prime number is 1609. The next prime is 1613 (a gap of 4) and the one before is 1607.
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 254th one is 1609.
- 2
1609 is prime because no prime up to ā1609 ā 40.11 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 254th prime is close to 254 Ć ln(254) ā 1406, and here it is 1609.
- 4
1609 is a twin prime: 1607 and 1609 are both prime.
Primes around the 254th
| Position | Prime | Gap from the previous |
|---|---|---|
| 251 | 1597 | 14 |
| 252 | 1601 | 4 |
| 253 | 1607 | 6 |
| 254 | 1609 | 2 |
| 255 | 1613 | 4 |
| 256 | 1619 | 6 |
| 257 | 1621 | 2 |
Questions
What is the 254th prime number?
1609.
Which prime number is 1609?
1609 is the 254th prime number.
What is the sum of the first 254 primes?
188,523.