What is the 3400th prime number?
The 3400th prime number is 31601. The next prime is 31607 (a gap of 6) and the one before is 31583.
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 3400th one is 31601.
- 2
31601 is prime because no prime up to ā31601 ā 177.77 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3400th prime is close to 3400 Ć ln(3400) ā 27647, and here it is 31601.
- 4
31601 has no twin: neither 31599 nor 31603 is prime.
Primes around the 3400th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3397 | 31567 | 20 |
| 3398 | 31573 | 6 |
| 3399 | 31583 | 10 |
| 3400 | 31601 | 18 |
| 3401 | 31607 | 6 |
| 3402 | 31627 | 20 |
| 3403 | 31643 | 16 |
Questions
What is the 3400th prime number?
31601.
Which prime number is 31601?
31601 is the 3400th prime number.
What is the sum of the first 3400 primes?
50,450,371.