What is the 670th prime number?
The 670th prime number is 5003. The next prime is 5009 (a gap of 6) and the one before is 4999.
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 670th one is 5003.
- 2
5003 is prime because no prime up to ā5003 ā 70.73 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 670th prime is close to 670 Ć ln(670) ā 4360, and here it is 5003.
- 4
5003 has no twin: neither 5001 nor 5005 is prime.
Primes around the 670th
| Position | Prime | Gap from the previous |
|---|---|---|
| 667 | 4987 | 14 |
| 668 | 4993 | 6 |
| 669 | 4999 | 6 |
| 670 | 5003 | 4 |
| 671 | 5009 | 6 |
| 672 | 5011 | 2 |
| 673 | 5021 | 10 |
Questions
What is the 670th prime number?
5003.
Which prime number is 5003?
5003 is the 670th prime number.
What is the sum of the first 670 primes?
1,553,139.