What is the 386th prime number?
The 386th prime number is 2663. The next prime is 2671 (a gap of 8) and the one before is 2659.
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 386th one is 2663.
- 2
2663 is prime because no prime up to ā2663 ā 51.60 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 386th prime is close to 386 Ć ln(386) ā 2299, and here it is 2663.
- 4
2663 has no twin: neither 2661 nor 2665 is prime.
Primes around the 386th
| Position | Prime | Gap from the previous |
|---|---|---|
| 383 | 2647 | 14 |
| 384 | 2657 | 10 |
| 385 | 2659 | 2 |
| 386 | 2663 | 4 |
| 387 | 2671 | 8 |
| 388 | 2677 | 6 |
| 389 | 2683 | 6 |
Questions
What is the 386th prime number?
2663.
Which prime number is 2663?
2663 is the 386th prime number.
What is the sum of the first 386 primes?
469,975.