What is the 667th prime number?
The 667th prime number is 4987. The next prime is 4993 (a gap of 6) and the one before is 4973.
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 667th one is 4987.
- 2
4987 is prime because no prime up to ā4987 ā 70.62 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 667th prime is close to 667 Ć ln(667) ā 4337, and here it is 4987.
- 4
4987 has no twin: neither 4985 nor 4989 is prime.
Primes around the 667th
| Position | Prime | Gap from the previous |
|---|---|---|
| 664 | 4967 | 10 |
| 665 | 4969 | 2 |
| 666 | 4973 | 4 |
| 667 | 4987 | 14 |
| 668 | 4993 | 6 |
| 669 | 4999 | 6 |
| 670 | 5003 | 4 |
Questions
What is the 667th prime number?
4987.
Which prime number is 4987?
4987 is the 667th prime number.
What is the sum of the first 667 primes?
1,538,144.