What is the 3650th prime number?
The 3650th prime number is 34157. The next prime is 34159 (a gap of 2) and the one before is 34147.
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 3650th one is 34157.
- 2
34157 is prime because no prime up to ā34157 ā 184.82 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3650th prime is close to 3650 Ć ln(3650) ā 29939, and here it is 34157.
- 4
34157 is a twin prime: 34157 and 34159 are both prime.
Primes around the 3650th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3647 | 34129 | 2 |
| 3648 | 34141 | 12 |
| 3649 | 34147 | 6 |
| 3650 | 34157 | 10 |
| 3651 | 34159 | 2 |
| 3652 | 34171 | 12 |
| 3653 | 34183 | 12 |
Questions
What is the 3650th prime number?
34157.
Which prime number is 34157?
34157 is the 3650th prime number.
What is the sum of the first 3650 primes?
58,671,101.