What is the 5000th prime number?
The 5000th prime number is 48611. The next prime is 48619 (a gap of 8) and the one before is 48593.
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 5000th one is 48611.
- 2
48611 is prime because no prime up to ā48611 ā 220.48 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 5000th prime is close to 5000 Ć ln(5000) ā 42586, and here it is 48611.
- 4
48611 has no twin: neither 48609 nor 48613 is prime.
Primes around the 5000th
| Position | Prime | Gap from the previous |
|---|---|---|
| 4997 | 48571 | 8 |
| 4998 | 48589 | 18 |
| 4999 | 48593 | 4 |
| 5000 | 48611 | 18 |
| 5001 | 48619 | 8 |
| 5002 | 48623 | 4 |
| 5003 | 48647 | 24 |
Questions
What is the 5000th prime number?
48611.
Which prime number is 48611?
48611 is the 5000th prime number.
What is the sum of the first 5000 primes?
114,455,259.