What is the 431st prime number?
The 431st prime number is 3001. The next prime is 3011 (a gap of 10) and the one before is 2999.
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 431st one is 3001.
- 2
3001 is prime because no prime up to ā3001 ā 54.78 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 431st prime is close to 431 Ć ln(431) ā 2614, and here it is 3001.
- 4
3001 is a twin prime: 2999 and 3001 are both prime.
Primes around the 431st
| Position | Prime | Gap from the previous |
|---|---|---|
| 428 | 2969 | 6 |
| 429 | 2971 | 2 |
| 430 | 2999 | 28 |
| 431 | 3001 | 2 |
| 432 | 3011 | 10 |
| 433 | 3019 | 8 |
| 434 | 3023 | 4 |
Questions
What is the 431st prime number?
3001.
Which prime number is 3001?
3001 is the 431st prime number.
What is the sum of the first 431 primes?
596,824.