The Sequence of Primes

function

sequence of primes

p

n

modulus

4

increment

1

range of n

100

The sequence of primes

p

n

generated by a simple algorithm like the sieve of Eratosthenes is not itself simple. The plots in this Demonstration show various features of the sequence that indicate that it is in many respects quite random. The logarithmic integral is defined by

li(z)=

z

∫

0

dt/logt

and the function

π(x)

counts the number of primes up to

x

.