What is the 851st prime number?
The 851st prime number is 6577. The next prime is 6581 (a gap of 4) and the one before is 6571.
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 851st one is 6577.
- 2
6577 is prime because no prime up to ā6577 ā 81.10 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 851st prime is close to 851 Ć ln(851) ā 5741, and here it is 6577.
- 4
6577 has no twin: neither 6575 nor 6579 is prime.
Primes around the 851st
| Position | Prime | Gap from the previous |
|---|---|---|
| 848 | 6563 | 10 |
| 849 | 6569 | 6 |
| 850 | 6571 | 2 |
| 851 | 6577 | 6 |
| 852 | 6581 | 4 |
| 853 | 6599 | 18 |
| 854 | 6607 | 8 |
Questions
What is the 851st prime number?
6577.
Which prime number is 6577?
6577 is the 851st prime number.
What is the sum of the first 851 primes?
2,602,118.