What is the 250th prime number?
The 250th prime number is 1583. The next prime is 1597 (a gap of 14) and the one before is 1579.
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 250th one is 1583.
- 2
1583 is prime because no prime up to ā1583 ā 39.79 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 250th prime is close to 250 Ć ln(250) ā 1380, and here it is 1583.
- 4
1583 has no twin: neither 1581 nor 1585 is prime.
Primes around the 250th
| Position | Prime | Gap from the previous |
|---|---|---|
| 247 | 1567 | 8 |
| 248 | 1571 | 4 |
| 249 | 1579 | 8 |
| 250 | 1583 | 4 |
| 251 | 1597 | 14 |
| 252 | 1601 | 4 |
| 253 | 1607 | 6 |
Questions
What is the 250th prime number?
1583.
Which prime number is 1583?
1583 is the 250th prime number.
What is the sum of the first 250 primes?
182,109.