What is the 3647th prime number?
The 3647th prime number is 34129. The next prime is 34141 (a gap of 12) and the one before is 34127.
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 3647th one is 34129.
- 2
34129 is prime because no prime up to ā34129 ā 184.74 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3647th prime is close to 3647 Ć ln(3647) ā 29911, and here it is 34129.
- 4
34129 is a twin prime: 34127 and 34129 are both prime.
Primes around the 3647th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3644 | 34061 | 4 |
| 3645 | 34123 | 62 |
| 3646 | 34127 | 4 |
| 3647 | 34129 | 2 |
| 3648 | 34141 | 12 |
| 3649 | 34147 | 6 |
| 3650 | 34157 | 10 |
Questions
What is the 3647th prime number?
34129.
Which prime number is 34129?
34129 is the 3647th prime number.
What is the sum of the first 3647 primes?
58,568,656.