What is the 72nd prime number?
The 72nd prime number is 359. The next prime is 367 (a gap of 8) and the one before is 353.
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 72nd one is 359.
- 2
359 is prime because no prime up to ā359 ā 18.95 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 72nd prime is close to 72 Ć ln(72) ā 308, and here it is 359.
- 4
359 has no twin: neither 357 nor 361 is prime.
Primes around the 72nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 69 | 347 | 10 |
| 70 | 349 | 2 |
| 71 | 353 | 4 |
| 72 | 359 | 6 |
| 73 | 367 | 8 |
| 74 | 373 | 6 |
| 75 | 379 | 6 |
Questions
What is the 72nd prime number?
359.
Which prime number is 359?
359 is the 72nd prime number.
What is the sum of the first 72 primes?
11,599.