What is the 3001st prime number?
The 3001st prime number is 27457. The next prime is 27479 (a gap of 22) and the one before is 27449.
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 3001st one is 27457.
- 2
27457 is prime because no prime up to ā27457 ā 165.70 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3001st prime is close to 3001 Ć ln(3001) ā 24028, and here it is 27457.
- 4
27457 has no twin: neither 27455 nor 27459 is prime.
Primes around the 3001st
| Position | Prime | Gap from the previous |
|---|---|---|
| 2998 | 27431 | 4 |
| 2999 | 27437 | 6 |
| 3000 | 27449 | 12 |
| 3001 | 27457 | 8 |
| 3002 | 27479 | 22 |
| 3003 | 27481 | 2 |
| 3004 | 27487 | 6 |
Questions
What is the 3001st prime number?
27457.
Which prime number is 27457?
27457 is the 3001st prime number.
What is the sum of the first 3001 primes?
38,672,668.