What is the 416th prime number?
The 416th prime number is 2861. The next prime is 2879 (a gap of 18) and the one before is 2857.
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 416th one is 2861.
- 2
2861 is prime because no prime up to ā2861 ā 53.49 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 416th prime is close to 416 Ć ln(416) ā 2509, and here it is 2861.
- 4
2861 has no twin: neither 2859 nor 2863 is prime.
Primes around the 416th
| Position | Prime | Gap from the previous |
|---|---|---|
| 413 | 2843 | 6 |
| 414 | 2851 | 8 |
| 415 | 2857 | 6 |
| 416 | 2861 | 4 |
| 417 | 2879 | 18 |
| 418 | 2887 | 8 |
| 419 | 2897 | 10 |
Questions
What is the 416th prime number?
2861.
Which prime number is 2861?
2861 is the 416th prime number.
What is the sum of the first 416 primes?
552,753.