What is the 2500th prime number?
The 2500th prime number is 22307. The next prime is 22343 (a gap of 36) and the one before is 22303.
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 2500th one is 22307.
- 2
22307 is prime because no prime up to ā22307 ā 149.36 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 2500th prime is close to 2500 Ć ln(2500) ā 19560, and here it is 22307.
- 4
22307 has no twin: neither 22305 nor 22309 is prime.
Primes around the 2500th
| Position | Prime | Gap from the previous |
|---|---|---|
| 2497 | 22283 | 4 |
| 2498 | 22291 | 8 |
| 2499 | 22303 | 12 |
| 2500 | 22307 | 4 |
| 2501 | 22343 | 36 |
| 2502 | 22349 | 6 |
| 2503 | 22367 | 18 |
Questions
What is the 2500th prime number?
22307.
Which prime number is 22307?
22307 is the 2500th prime number.
What is the sum of the first 2500 primes?
26,211,025.