What is the 671st prime number?
The 671st prime number is 5009. The next prime is 5011 (a gap of 2) and the one before is 5003.
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 671st one is 5009.
- 2
5009 is prime because no prime up to ā5009 ā 70.77 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 671st prime is close to 671 Ć ln(671) ā 4367, and here it is 5009.
- 4
5009 is a twin prime: 5009 and 5011 are both prime.
Primes around the 671st
| Position | Prime | Gap from the previous |
|---|---|---|
| 668 | 4993 | 6 |
| 669 | 4999 | 6 |
| 670 | 5003 | 4 |
| 671 | 5009 | 6 |
| 672 | 5011 | 2 |
| 673 | 5021 | 10 |
| 674 | 5023 | 2 |
Questions
What is the 671st prime number?
5009.
Which prime number is 5009?
5009 is the 671st prime number.
What is the sum of the first 671 primes?
1,558,148.