What is the 7000th prime number?
The 7000th prime number is 70657. The next prime is 70663 (a gap of 6) and the one before is 70639.
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 7000th one is 70657.
- 2
70657 is prime because no prime up to ā70657 ā 265.81 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 7000th prime is close to 7000 Ć ln(7000) ā 61976, and here it is 70657.
- 4
70657 has no twin: neither 70655 nor 70659 is prime.
Primes around the 7000th
| Position | Prime | Gap from the previous |
|---|---|---|
| 6997 | 70621 | 2 |
| 6998 | 70627 | 6 |
| 6999 | 70639 | 12 |
| 7000 | 70657 | 18 |
| 7001 | 70663 | 6 |
| 7002 | 70667 | 4 |
| 7003 | 70687 | 20 |
Questions
What is the 7000th prime number?
70657.
Which prime number is 70657?
70657 is the 7000th prime number.
What is the sum of the first 7000 primes?
233,461,073.