What is the 400th prime number?
The 400th prime number is 2741. The next prime is 2749 (a gap of 8) and the one before is 2731.
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 400th one is 2741.
- 2
2741 is prime because no prime up to ā2741 ā 52.35 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 400th prime is close to 400 Ć ln(400) ā 2397, and here it is 2741.
- 4
2741 has no twin: neither 2739 nor 2743 is prime.
Primes around the 400th
| Position | Prime | Gap from the previous |
|---|---|---|
| 397 | 2719 | 6 |
| 398 | 2729 | 10 |
| 399 | 2731 | 2 |
| 400 | 2741 | 10 |
| 401 | 2749 | 8 |
| 402 | 2753 | 4 |
| 403 | 2767 | 14 |
Questions
What is the 400th prime number?
2741.
Which prime number is 2741?
2741 is the 400th prime number.
What is the sum of the first 400 primes?
507,825.