What is the 3701st prime number?
The 3701st prime number is 34651. The next prime is 34667 (a gap of 16) and the one before is 34649.
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 3701st one is 34651.
- 2
34651 is prime because no prime up to ā34651 ā 186.15 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3701st prime is close to 3701 Ć ln(3701) ā 30409, and here it is 34651.
- 4
34651 is a twin prime: 34649 and 34651 are both prime.
Primes around the 3701st
| Position | Prime | Gap from the previous |
|---|---|---|
| 3698 | 34613 | 6 |
| 3699 | 34631 | 18 |
| 3700 | 34649 | 18 |
| 3701 | 34651 | 2 |
| 3702 | 34667 | 16 |
| 3703 | 34673 | 6 |
| 3704 | 34679 | 6 |
Questions
What is the 3701st prime number?
34651.
Which prime number is 34651?
34651 is the 3701st prime number.
What is the sum of the first 3701 primes?
60,425,856.