What is the 428th prime number?
The 428th prime number is 2969. The next prime is 2971 (a gap of 2) and the one before is 2963.
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 428th one is 2969.
- 2
2969 is prime because no prime up to ā2969 ā 54.49 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 428th prime is close to 428 Ć ln(428) ā 2593, and here it is 2969.
- 4
2969 is a twin prime: 2969 and 2971 are both prime.
Primes around the 428th
| Position | Prime | Gap from the previous |
|---|---|---|
| 425 | 2953 | 14 |
| 426 | 2957 | 4 |
| 427 | 2963 | 6 |
| 428 | 2969 | 6 |
| 429 | 2971 | 2 |
| 430 | 2999 | 28 |
| 431 | 3001 | 2 |
Questions
What is the 428th prime number?
2969.
Which prime number is 2969?
2969 is the 428th prime number.
What is the sum of the first 428 primes?
587,853.