What is the 301st prime number?
The 301st prime number is 1993. The next prime is 1997 (a gap of 4) and the one before is 1987.
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 301st one is 1993.
- 2
1993 is prime because no prime up to ā1993 ā 44.64 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 301st prime is close to 301 Ć ln(301) ā 1718, and here it is 1993.
- 4
1993 has no twin: neither 1991 nor 1995 is prime.
Primes around the 301st
| Position | Prime | Gap from the previous |
|---|---|---|
| 298 | 1973 | 22 |
| 299 | 1979 | 6 |
| 300 | 1987 | 8 |
| 301 | 1993 | 6 |
| 302 | 1997 | 4 |
| 303 | 1999 | 2 |
| 304 | 2003 | 4 |
Questions
What is the 301st prime number?
1993.
Which prime number is 1993?
1993 is the 301st prime number.
What is the sum of the first 301 primes?
273,054.