What is the 365th prime number?
The 365th prime number is 2467. The next prime is 2473 (a gap of 6) and the one before is 2459.
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 365th one is 2467.
- 2
2467 is prime because no prime up to ā2467 ā 49.67 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 365th prime is close to 365 Ć ln(365) ā 2153, and here it is 2467.
- 4
2467 has no twin: neither 2465 nor 2469 is prime.
Primes around the 365th
| Position | Prime | Gap from the previous |
|---|---|---|
| 362 | 2441 | 4 |
| 363 | 2447 | 6 |
| 364 | 2459 | 12 |
| 365 | 2467 | 8 |
| 366 | 2473 | 6 |
| 367 | 2477 | 4 |
| 368 | 2503 | 26 |
Questions
What is the 365th prime number?
2467.
Which prime number is 2467?
2467 is the 365th prime number.
What is the sum of the first 365 primes?
415,862.