What is the 4072nd prime number?
The 4072nd prime number is 38653. The next prime is 38669 (a gap of 16) and the one before is 38651.
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 4072nd one is 38653.
- 2
38653 is prime because no prime up to ā38653 ā 196.60 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 4072nd prime is close to 4072 Ć ln(4072) ā 33846, and here it is 38653.
- 4
38653 is a twin prime: 38651 and 38653 are both prime.
Primes around the 4072nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 4069 | 38629 | 18 |
| 4070 | 38639 | 10 |
| 4071 | 38651 | 12 |
| 4072 | 38653 | 2 |
| 4073 | 38669 | 16 |
| 4074 | 38671 | 2 |
| 4075 | 38677 | 6 |
Questions
What is the 4072nd prime number?
38653.
Which prime number is 38653?
38653 is the 4072nd prime number.
What is the sum of the first 4072 primes?
74,020,233.