What is the 85th prime number?
The 85th prime number is 439. The next prime is 443 (a gap of 4) and the one before is 433.
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 85th one is 439.
- 2
439 is prime because no prime up to ā439 ā 20.95 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 85th prime is close to 85 Ć ln(85) ā 378, and here it is 439.
- 4
439 has no twin: neither 437 nor 441 is prime.
Primes around the 85th
| Position | Prime | Gap from the previous |
|---|---|---|
| 82 | 421 | 2 |
| 83 | 431 | 10 |
| 84 | 433 | 2 |
| 85 | 439 | 6 |
| 86 | 443 | 4 |
| 87 | 449 | 6 |
| 88 | 457 | 8 |
Questions
What is the 85th prime number?
439.
Which prime number is 439?
439 is the 85th prime number.
What is the sum of the first 85 primes?
16,840.