What is the 3000th prime number?
The 3000th prime number is 27449. The next prime is 27457 (a gap of 8) and the one before is 27437.
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 3000th one is 27449.
- 2
27449 is prime because no prime up to ā27449 ā 165.68 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3000th prime is close to 3000 Ć ln(3000) ā 24019, and here it is 27449.
- 4
27449 has no twin: neither 27447 nor 27451 is prime.
Primes around the 3000th
| Position | Prime | Gap from the previous |
|---|---|---|
| 2997 | 27427 | 18 |
| 2998 | 27431 | 4 |
| 2999 | 27437 | 6 |
| 3000 | 27449 | 12 |
| 3001 | 27457 | 8 |
| 3002 | 27479 | 22 |
| 3003 | 27481 | 2 |
Questions
What is the 3000th prime number?
27449.
Which prime number is 27449?
27449 is the 3000th prime number.
What is the sum of the first 3000 primes?
38,645,211.