What is the 3420th prime number?
The 3420th prime number is 31817. The next prime is 31847 (a gap of 30) and the one before is 31799.
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 3420th one is 31817.
- 2
31817 is prime because no prime up to ā31817 ā 178.37 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3420th prime is close to 3420 Ć ln(3420) ā 27830, and here it is 31817.
- 4
31817 has no twin: neither 31815 nor 31819 is prime.
Primes around the 3420th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3417 | 31771 | 2 |
| 3418 | 31793 | 22 |
| 3419 | 31799 | 6 |
| 3420 | 31817 | 18 |
| 3421 | 31847 | 30 |
| 3422 | 31849 | 2 |
| 3423 | 31859 | 10 |
Questions
What is the 3420th prime number?
31817.
Which prime number is 31817?
31817 is the 3420th prime number.
What is the sum of the first 3420 primes?
51,084,611.