What is the 402nd prime number?
The 402nd prime number is 2753. The next prime is 2767 (a gap of 14) and the one before is 2749.
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 402nd one is 2753.
- 2
2753 is prime because no prime up to ā2753 ā 52.47 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 402nd prime is close to 402 Ć ln(402) ā 2411, and here it is 2753.
- 4
2753 has no twin: neither 2751 nor 2755 is prime.
Primes around the 402nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 399 | 2731 | 2 |
| 400 | 2741 | 10 |
| 401 | 2749 | 8 |
| 402 | 2753 | 4 |
| 403 | 2767 | 14 |
| 404 | 2777 | 10 |
| 405 | 2789 | 12 |
Questions
What is the 402nd prime number?
2753.
Which prime number is 2753?
2753 is the 402nd prime number.
What is the sum of the first 402 primes?
513,327.