What is the 420th prime number?
The 420th prime number is 2903. The next prime is 2909 (a gap of 6) and the one before is 2897.
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 420th one is 2903.
- 2
2903 is prime because no prime up to ā2903 ā 53.88 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 420th prime is close to 420 Ć ln(420) ā 2537, and here it is 2903.
- 4
2903 has no twin: neither 2901 nor 2905 is prime.
Primes around the 420th
| Position | Prime | Gap from the previous |
|---|---|---|
| 417 | 2879 | 18 |
| 418 | 2887 | 8 |
| 419 | 2897 | 10 |
| 420 | 2903 | 6 |
| 421 | 2909 | 6 |
| 422 | 2917 | 8 |
| 423 | 2927 | 10 |
Questions
What is the 420th prime number?
2903.
Which prime number is 2903?
2903 is the 420th prime number.
What is the sum of the first 420 primes?
564,319.