What is the 3403rd prime number?
The 3403rd prime number is 31643. The next prime is 31649 (a gap of 6) and the one before is 31627.
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 3403rd one is 31643.
- 2
31643 is prime because no prime up to ā31643 ā 177.88 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3403rd prime is close to 3403 Ć ln(3403) ā 27675, and here it is 31643.
- 4
31643 has no twin: neither 31641 nor 31645 is prime.
Primes around the 3403rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 3400 | 31601 | 18 |
| 3401 | 31607 | 6 |
| 3402 | 31627 | 20 |
| 3403 | 31643 | 16 |
| 3404 | 31649 | 6 |
| 3405 | 31657 | 8 |
| 3406 | 31663 | 6 |
Questions
What is the 3403rd prime number?
31643.
Which prime number is 31643?
31643 is the 3403rd prime number.
What is the sum of the first 3403 primes?
50,545,248.