What is the 302nd prime number?
The 302nd prime number is 1997. The next prime is 1999 (a gap of 2) and the one before is 1993.
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 302nd one is 1997.
- 2
1997 is prime because no prime up to ā1997 ā 44.69 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 302nd prime is close to 302 Ć ln(302) ā 1725, and here it is 1997.
- 4
1997 is a twin prime: 1997 and 1999 are both prime.
Primes around the 302nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 299 | 1979 | 6 |
| 300 | 1987 | 8 |
| 301 | 1993 | 6 |
| 302 | 1997 | 4 |
| 303 | 1999 | 2 |
| 304 | 2003 | 4 |
| 305 | 2011 | 8 |
Questions
What is the 302nd prime number?
1997.
Which prime number is 1997?
1997 is the 302nd prime number.
What is the sum of the first 302 primes?
275,051.