What is the 253rd prime number?
The 253rd prime number is 1607. The next prime is 1609 (a gap of 2) and the one before is 1601.
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 253rd one is 1607.
- 2
1607 is prime because no prime up to ā1607 ā 40.09 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 253rd prime is close to 253 Ć ln(253) ā 1400, and here it is 1607.
- 4
1607 is a twin prime: 1607 and 1609 are both prime.
Primes around the 253rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 250 | 1583 | 4 |
| 251 | 1597 | 14 |
| 252 | 1601 | 4 |
| 253 | 1607 | 6 |
| 254 | 1609 | 2 |
| 255 | 1613 | 4 |
| 256 | 1619 | 6 |
Questions
What is the 253rd prime number?
1607.
Which prime number is 1607?
1607 is the 253rd prime number.
What is the sum of the first 253 primes?
186,914.