What is the 415th prime number?
The 415th prime number is 2857. The next prime is 2861 (a gap of 4) and the one before is 2851.
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 415th one is 2857.
- 2
2857 is prime because no prime up to ā2857 ā 53.45 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 415th prime is close to 415 Ć ln(415) ā 2502, and here it is 2857.
- 4
2857 has no twin: neither 2855 nor 2859 is prime.
Primes around the 415th
| Position | Prime | Gap from the previous |
|---|---|---|
| 412 | 2837 | 4 |
| 413 | 2843 | 6 |
| 414 | 2851 | 8 |
| 415 | 2857 | 6 |
| 416 | 2861 | 4 |
| 417 | 2879 | 18 |
| 418 | 2887 | 8 |
Questions
What is the 415th prime number?
2857.
Which prime number is 2857?
2857 is the 415th prime number.
What is the sum of the first 415 primes?
549,892.