What is the 429th prime number?
The 429th prime number is 2971. The next prime is 2999 (a gap of 28) and the one before is 2969.
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 429th one is 2971.
- 2
2971 is prime because no prime up to ā2971 ā 54.51 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 429th prime is close to 429 Ć ln(429) ā 2600, and here it is 2971.
- 4
2971 is a twin prime: 2969 and 2971 are both prime.
Primes around the 429th
| Position | Prime | Gap from the previous |
|---|---|---|
| 426 | 2957 | 4 |
| 427 | 2963 | 6 |
| 428 | 2969 | 6 |
| 429 | 2971 | 2 |
| 430 | 2999 | 28 |
| 431 | 3001 | 2 |
| 432 | 3011 | 10 |
Questions
What is the 429th prime number?
2971.
Which prime number is 2971?
2971 is the 429th prime number.
What is the sum of the first 429 primes?
590,824.