Prime number or not?
The number above has 2016 zeros. Is this number a prime number or a composite number?
Note that the digits 1 and 0 alternate.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
We use the formula for the sum of the first n terms of a geometric series. k = 0 ∑ n q k = q − 1 q n + 1 − 1 . Let us denote the given number as Z 2 0 1 6 .
Z 2 0 1 6 = k = 0 ∑ 2 0 1 6 ( 1 0 2 ) k = 1 0 0 − 1 ( 1 0 2 ) 2 0 1 7 − 1 = 9 • 1 1 ( 1 0 2 0 1 7 ) 2 − 1 = 9 1 0 2 0 1 7 − 1 • 1 1 1 0 2 0 1 7 + 1 = i = 0 ∑ 2 0 1 6 1 0 i • i = 0 ∑ 2 0 1 6 − 1 0 i . Both factors are natural numbers because they are sums of natural numbers. The first factor is bigger than 1 and smaller than Z 2 0 1 6 . Therefore Z 2 0 1 6 is not a prime.