What is the 631st prime number?
The 631st prime number is 4663. The next prime is 4673 (a gap of 10) and the one before is 4657.
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 631st one is 4663.
- 2
4663 is prime because no prime up to ā4663 ā 68.29 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 631st prime is close to 631 Ć ln(631) ā 4068, and here it is 4663.
- 4
4663 has no twin: neither 4661 nor 4665 is prime.
Primes around the 631st
| Position | Prime | Gap from the previous |
|---|---|---|
| 628 | 4649 | 6 |
| 629 | 4651 | 2 |
| 630 | 4657 | 6 |
| 631 | 4663 | 6 |
| 632 | 4673 | 10 |
| 633 | 4679 | 6 |
| 634 | 4691 | 12 |
Questions
What is the 631st prime number?
4663.
Which prime number is 4663?
4663 is the 631st prime number.
What is the sum of the first 631 primes?
1,363,992.