What is the 401st prime number?
The 401st prime number is 2749. The next prime is 2753 (a gap of 4) and the one before is 2741.
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 401st one is 2749.
- 2
2749 is prime because no prime up to ā2749 ā 52.43 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 401st prime is close to 401 Ć ln(401) ā 2404, and here it is 2749.
- 4
2749 has no twin: neither 2747 nor 2751 is prime.
Primes around the 401st
| Position | Prime | Gap from the previous |
|---|---|---|
| 398 | 2729 | 10 |
| 399 | 2731 | 2 |
| 400 | 2741 | 10 |
| 401 | 2749 | 8 |
| 402 | 2753 | 4 |
| 403 | 2767 | 14 |
| 404 | 2777 | 10 |
Questions
What is the 401st prime number?
2749.
Which prime number is 2749?
2749 is the 401st prime number.
What is the sum of the first 401 primes?
510,574.