What is the 78th prime number?
The 78th prime number is 397. The next prime is 401 (a gap of 4) and the one before is 389.
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 78th one is 397.
- 2
397 is prime because no prime up to ā397 ā 19.92 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 78th prime is close to 78 Ć ln(78) ā 340, and here it is 397.
- 4
397 has no twin: neither 395 nor 399 is prime.
Primes around the 78th
| Position | Prime | Gap from the previous |
|---|---|---|
| 75 | 379 | 6 |
| 76 | 383 | 4 |
| 77 | 389 | 6 |
| 78 | 397 | 8 |
| 79 | 401 | 4 |
| 80 | 409 | 8 |
| 81 | 419 | 10 |
Questions
What is the 78th prime number?
397.
Which prime number is 397?
397 is the 78th prime number.
What is the sum of the first 78 primes?
13,887.