What is the 300th prime number?
The 300th prime number is 1987. The next prime is 1993 (a gap of 6) and the one before is 1979.
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 300th one is 1987.
- 2
1987 is prime because no prime up to ā1987 ā 44.58 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 300th prime is close to 300 Ć ln(300) ā 1711, and here it is 1987.
- 4
1987 has no twin: neither 1985 nor 1989 is prime.
Primes around the 300th
| Position | Prime | Gap from the previous |
|---|---|---|
| 297 | 1951 | 2 |
| 298 | 1973 | 22 |
| 299 | 1979 | 6 |
| 300 | 1987 | 8 |
| 301 | 1993 | 6 |
| 302 | 1997 | 4 |
| 303 | 1999 | 2 |
Questions
What is the 300th prime number?
1987.
Which prime number is 1987?
1987 is the 300th prime number.
What is the sum of the first 300 primes?
271,061.