What is the 10000th prime number?
The 10000th prime number is 104729. The next prime is 104743 (a gap of 14) and the one before is 104723.
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 10000th one is 104729.
- 2
104729 is prime because no prime up to ā104729 ā 323.62 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 10000th prime is close to 10000 Ć ln(10000) ā 92103, and here it is 104729.
- 4
104729 has no twin: neither 104727 nor 104731 is prime.
Primes around the 10000th
| Position | Prime | Gap from the previous |
|---|---|---|
| 9997 | 104711 | 4 |
| 9998 | 104717 | 6 |
| 9999 | 104723 | 6 |
| 10000 | 104729 | 6 |
| 10001 | 104743 | 14 |
| 10002 | 104759 | 16 |
| 10003 | 104761 | 2 |
Questions
What is the 10000th prime number?
104729.
Which prime number is 104729?
104729 is the 10000th prime number.
What is the sum of the first 10000 primes?
496,165,411.