What is the 657th prime number?
The 657th prime number is 4919. The next prime is 4931 (a gap of 12) and the one before is 4909.
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 657th one is 4919.
- 2
4919 is prime because no prime up to ā4919 ā 70.14 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 657th prime is close to 657 Ć ln(657) ā 4262, and here it is 4919.
- 4
4919 has no twin: neither 4917 nor 4921 is prime.
Primes around the 657th
| Position | Prime | Gap from the previous |
|---|---|---|
| 654 | 4889 | 12 |
| 655 | 4903 | 14 |
| 656 | 4909 | 6 |
| 657 | 4919 | 10 |
| 658 | 4931 | 12 |
| 659 | 4933 | 2 |
| 660 | 4937 | 4 |
Questions
What is the 657th prime number?
4919.
Which prime number is 4919?
4919 is the 657th prime number.
What is the sum of the first 657 primes?
1,488,596.