What is the 2564th prime number?
The 2564th prime number is 22993. The next prime is 23003 (a gap of 10) and the one before is 22973.
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 2564th one is 22993.
- 2
22993 is prime because no prime up to ā22993 ā 151.63 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 2564th prime is close to 2564 Ć ln(2564) ā 20126, and here it is 22993.
- 4
22993 has no twin: neither 22991 nor 22995 is prime.
Primes around the 2564th
| Position | Prime | Gap from the previous |
|---|---|---|
| 2561 | 22961 | 18 |
| 2562 | 22963 | 2 |
| 2563 | 22973 | 10 |
| 2564 | 22993 | 20 |
| 2565 | 23003 | 10 |
| 2566 | 23011 | 8 |
| 2567 | 23017 | 6 |
Questions
What is the 2564th prime number?
22993.
Which prime number is 22993?
22993 is the 2564th prime number.
What is the sum of the first 2564 primes?
27,661,459.