What is the 3970th prime number?
The 3970th prime number is 37507. The next prime is 37511 (a gap of 4) and the one before is 37501.
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 3970th one is 37507.
- 2
37507 is prime because no prime up to ā37507 ā 193.67 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3970th prime is close to 3970 Ć ln(3970) ā 32897, and here it is 37507.
- 4
37507 has no twin: neither 37505 nor 37509 is prime.
Primes around the 3970th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3967 | 37489 | 6 |
| 3968 | 37493 | 4 |
| 3969 | 37501 | 8 |
| 3970 | 37507 | 6 |
| 3971 | 37511 | 4 |
| 3972 | 37517 | 6 |
| 3973 | 37529 | 12 |
Questions
What is the 3970th prime number?
37507.
Which prime number is 37507?
37507 is the 3970th prime number.
What is the sum of the first 3970 primes?
70,137,681.