What is the 3780th prime number?
The 3780th prime number is 35509. The next prime is 35521 (a gap of 12) and the one before is 35507.
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 3780th one is 35509.
- 2
35509 is prime because no prime up to ā35509 ā 188.44 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3780th prime is close to 3780 Ć ln(3780) ā 31138, and here it is 35509.
- 4
35509 is a twin prime: 35507 and 35509 are both prime.
Primes around the 3780th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3777 | 35461 | 12 |
| 3778 | 35491 | 30 |
| 3779 | 35507 | 16 |
| 3780 | 35509 | 2 |
| 3781 | 35521 | 12 |
| 3782 | 35527 | 6 |
| 3783 | 35531 | 4 |
Questions
What is the 3780th prime number?
35509.
Which prime number is 35509?
35509 is the 3780th prime number.
What is the sum of the first 3780 primes?
63,197,317.