What is the 403rd prime number?
The 403rd prime number is 2767. The next prime is 2777 (a gap of 10) and the one before is 2753.
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 403rd one is 2767.
- 2
2767 is prime because no prime up to ā2767 ā 52.60 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 403rd prime is close to 403 Ć ln(403) ā 2418, and here it is 2767.
- 4
2767 has no twin: neither 2765 nor 2769 is prime.
Primes around the 403rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 400 | 2741 | 10 |
| 401 | 2749 | 8 |
| 402 | 2753 | 4 |
| 403 | 2767 | 14 |
| 404 | 2777 | 10 |
| 405 | 2789 | 12 |
| 406 | 2791 | 2 |
Questions
What is the 403rd prime number?
2767.
Which prime number is 2767?
2767 is the 403rd prime number.
What is the sum of the first 403 primes?
516,094.