What is the 3401st prime number?
The 3401st prime number is 31607. The next prime is 31627 (a gap of 20) and the one before is 31601.
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 3401st one is 31607.
- 2
31607 is prime because no prime up to ā31607 ā 177.78 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3401st prime is close to 3401 Ć ln(3401) ā 27656, and here it is 31607.
- 4
31607 has no twin: neither 31605 nor 31609 is prime.
Primes around the 3401st
| Position | Prime | Gap from the previous |
|---|---|---|
| 3398 | 31573 | 6 |
| 3399 | 31583 | 10 |
| 3400 | 31601 | 18 |
| 3401 | 31607 | 6 |
| 3402 | 31627 | 20 |
| 3403 | 31643 | 16 |
| 3404 | 31649 | 6 |
Questions
What is the 3401st prime number?
31607.
Which prime number is 31607?
31607 is the 3401st prime number.
What is the sum of the first 3401 primes?
50,481,978.