What is the 3301st prime number?
The 3301st prime number is 30577. The next prime is 30593 (a gap of 16) and the one before is 30559.
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 3301st one is 30577.
- 2
30577 is prime because no prime up to ā30577 ā 174.86 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3301st prime is close to 3301 Ć ln(3301) ā 26745, and here it is 30577.
- 4
30577 has no twin: neither 30575 nor 30579 is prime.
Primes around the 3301st
| Position | Prime | Gap from the previous |
|---|---|---|
| 3298 | 30553 | 14 |
| 3299 | 30557 | 4 |
| 3300 | 30559 | 2 |
| 3301 | 30577 | 18 |
| 3302 | 30593 | 16 |
| 3303 | 30631 | 38 |
| 3304 | 30637 | 6 |
Questions
What is the 3301st prime number?
30577.
Which prime number is 30577?
30577 is the 3301st prime number.
What is the sum of the first 3301 primes?
47,371,906.