What is the 86th prime number?
The 86th prime number is 443. The next prime is 449 (a gap of 6) and the one before is 439.
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 86th one is 443.
- 2
443 is prime because no prime up to ā443 ā 21.05 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 86th prime is close to 86 Ć ln(86) ā 383, and here it is 443.
- 4
443 has no twin: neither 441 nor 445 is prime.
Primes around the 86th
| Position | Prime | Gap from the previous |
|---|---|---|
| 83 | 431 | 10 |
| 84 | 433 | 2 |
| 85 | 439 | 6 |
| 86 | 443 | 4 |
| 87 | 449 | 6 |
| 88 | 457 | 8 |
| 89 | 461 | 4 |
Questions
What is the 86th prime number?
443.
Which prime number is 443?
443 is the 86th prime number.
What is the sum of the first 86 primes?
17,283.