It is known that 11 is a prime. Does any prime numbers of the form n times 1 1 1 … 1 , where n > 2 , exist?
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.
Next prime is 23 times 1 1 1 ⋯ 1 1 .
Log in to reply
Values for n such that those numbers are prime are
2 , 1 9 , 2 3 , 3 1 7 , 1 0 3 1 , 4 9 0 8 1 , 8 6 4 5 3 , 1 0 9 2 9 7 , 2 7 0 3 4 3 . . .
but only the first five are proven to be primes. The others are only "probable primes".
Any proof for existence?
Problem Loading...
Note Loading...
Set Loading...
Note that 1 9 times 1 1 … 1 = ∑ k = 0 1 8 1 0 k is a prime.
There is a conjecture that there are infinite many primes of the form n times 1 1 … 1 .