What is the 3700th prime number?
The 3700th prime number is 34649. The next prime is 34651 (a gap of 2) and the one before is 34631.
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 3700th one is 34649.
- 2
34649 is prime because no prime up to ā34649 ā 186.14 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3700th prime is close to 3700 Ć ln(3700) ā 30400, and here it is 34649.
- 4
34649 is a twin prime: 34649 and 34651 are both prime.
Primes around the 3700th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3697 | 34607 | 4 |
| 3698 | 34613 | 6 |
| 3699 | 34631 | 18 |
| 3700 | 34649 | 18 |
| 3701 | 34651 | 2 |
| 3702 | 34667 | 16 |
| 3703 | 34673 | 6 |
Questions
What is the 3700th prime number?
34649.
Which prime number is 34649?
34649 is the 3700th prime number.
What is the sum of the first 3700 primes?
60,391,205.