What is the 251st prime number?
The 251st prime number is 1597. The next prime is 1601 (a gap of 4) and the one before is 1583.
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 251st one is 1597.
- 2
1597 is prime because no prime up to ā1597 ā 39.96 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 251st prime is close to 251 Ć ln(251) ā 1387, and here it is 1597.
- 4
1597 has no twin: neither 1595 nor 1599 is prime.
Primes around the 251st
| Position | Prime | Gap from the previous |
|---|---|---|
| 248 | 1571 | 4 |
| 249 | 1579 | 8 |
| 250 | 1583 | 4 |
| 251 | 1597 | 14 |
| 252 | 1601 | 4 |
| 253 | 1607 | 6 |
| 254 | 1609 | 2 |
Questions
What is the 251st prime number?
1597.
Which prime number is 1597?
1597 is the 251st prime number.
What is the sum of the first 251 primes?
183,706.