What is the 252nd prime number?
The 252nd prime number is 1601. The next prime is 1607 (a gap of 6) and the one before is 1597.
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 252nd one is 1601.
- 2
1601 is prime because no prime up to ā1601 ā 40.01 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 252nd prime is close to 252 Ć ln(252) ā 1393, and here it is 1601.
- 4
1601 has no twin: neither 1599 nor 1603 is prime.
Primes around the 252nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 249 | 1579 | 8 |
| 250 | 1583 | 4 |
| 251 | 1597 | 14 |
| 252 | 1601 | 4 |
| 253 | 1607 | 6 |
| 254 | 1609 | 2 |
| 255 | 1613 | 4 |
Questions
What is the 252nd prime number?
1601.
Which prime number is 1601?
1601 is the 252nd prime number.
What is the sum of the first 252 primes?
185,307.