What is the 8142nd prime number?
The 8142nd prime number is 83407. The next prime is 83417 (a gap of 10) and the one before is 83401.
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 8142nd one is 83407.
- 2
83407 is prime because no prime up to ā83407 ā 288.80 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 8142nd prime is close to 8142 Ć ln(8142) ā 73317, and here it is 83407.
- 4
83407 has no twin: neither 83405 nor 83409 is prime.
Primes around the 8142nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 8139 | 83389 | 6 |
| 8140 | 83399 | 10 |
| 8141 | 83401 | 2 |
| 8142 | 83407 | 6 |
| 8143 | 83417 | 10 |
| 8144 | 83423 | 6 |
| 8145 | 83431 | 8 |
Questions
What is the 8142nd prime number?
83407.
Which prime number is 83407?
83407 is the 8142nd prime number.
What is the sum of the first 8142 primes?
321,404,965.