What is the 1400th prime number?
The 1400th prime number is 11657. The next prime is 11677 (a gap of 20) and the one before is 11633.
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 1400th one is 11657.
- 2
11657 is prime because no prime up to ā11657 ā 107.97 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 1400th prime is close to 1400 Ć ln(1400) ā 10142, and here it is 11657.
- 4
11657 has no twin: neither 11655 nor 11659 is prime.
Primes around the 1400th
| Position | Prime | Gap from the previous |
|---|---|---|
| 1397 | 11617 | 20 |
| 1398 | 11621 | 4 |
| 1399 | 11633 | 12 |
| 1400 | 11657 | 24 |
| 1401 | 11677 | 20 |
| 1402 | 11681 | 4 |
| 1403 | 11689 | 8 |
Questions
What is the 1400th prime number?
11657.
Which prime number is 11657?
11657 is the 1400th prime number.
What is the sum of the first 1400 primes?
7,584,569.