What is the 1300th prime number?
The 1300th prime number is 10657. The next prime is 10663 (a gap of 6) and the one before is 10651.
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 1300th one is 10657.
- 2
10657 is prime because no prime up to ā10657 ā 103.23 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 1300th prime is close to 1300 Ć ln(1300) ā 9321, and here it is 10657.
- 4
10657 has no twin: neither 10655 nor 10659 is prime.
Primes around the 1300th
| Position | Prime | Gap from the previous |
|---|---|---|
| 1297 | 10631 | 4 |
| 1298 | 10639 | 8 |
| 1299 | 10651 | 12 |
| 1300 | 10657 | 6 |
| 1301 | 10663 | 6 |
| 1302 | 10667 | 4 |
| 1303 | 10687 | 20 |
Questions
What is the 1300th prime number?
10657.
Which prime number is 10657?
10657 is the 1300th prime number.
What is the sum of the first 1300 primes?
6,469,497.