What is the 2561st prime number?
The 2561st prime number is 22961. The next prime is 22963 (a gap of 2) and the one before is 22943.
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 2561st one is 22961.
- 2
22961 is prime because no prime up to ā22961 ā 151.53 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 2561st prime is close to 2561 Ć ln(2561) ā 20099, and here it is 22961.
- 4
22961 is a twin prime: 22961 and 22963 are both prime.
Primes around the 2561st
| Position | Prime | Gap from the previous |
|---|---|---|
| 2558 | 22921 | 14 |
| 2559 | 22937 | 16 |
| 2560 | 22943 | 6 |
| 2561 | 22961 | 18 |
| 2562 | 22963 | 2 |
| 2563 | 22973 | 10 |
| 2564 | 22993 | 20 |
Questions
What is the 2561st prime number?
22961.
Which prime number is 22961?
22961 is the 2561st prime number.
What is the sum of the first 2561 primes?
27,592,530.