What is the 364th prime number?
The 364th prime number is 2459. The next prime is 2467 (a gap of 8) and the one before is 2447.
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 364th one is 2459.
- 2
2459 is prime because no prime up to ā2459 ā 49.59 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 364th prime is close to 364 Ć ln(364) ā 2147, and here it is 2459.
- 4
2459 has no twin: neither 2457 nor 2461 is prime.
Primes around the 364th
| Position | Prime | Gap from the previous |
|---|---|---|
| 361 | 2437 | 14 |
| 362 | 2441 | 4 |
| 363 | 2447 | 6 |
| 364 | 2459 | 12 |
| 365 | 2467 | 8 |
| 366 | 2473 | 6 |
| 367 | 2477 | 4 |
Questions
What is the 364th prime number?
2459.
Which prime number is 2459?
2459 is the 364th prime number.
What is the sum of the first 364 primes?
413,395.