| |
|
 |
|
Gauss
changed the question: Instead of "where is
the next prime?" he asked "how many
primes are there less than 10, 100, 1000 or any
number N?"
| N |
Number of primes from 1 up to
N, often referred to as 
(N) |
On average, how many numbers
you need to count before you expect a prime
number |
| 10 |
4 |
2.5 |
| 100 |
25 |
4.0 |
| 1,000 |
168 |
6.0 |
| 10,000 |
1,229 |
8.1 |
| 100,000 |
9,592 |
10.4 |
| 1,000,000 |
78,498 |
12.7 |
| 10,000,000 |
664,579 |
15.0 |
| 100,000,000 |
5,761,455 |
17.4 |
| 1,000,000,000 |
50,847,534 |
19.7 |
| 10,000,000,000 |
455,052,511 |
22.0 |
The last column shows the
probability that a number chosen at random around
N is a prime number.
|
|
