Prime number?

It is known that 11 is a prime. Does any prime numbers of the form 111 1 n times \underbrace{111\ldots 1}_{n \,\text{times}} , where n > 2 n>2 , exist?

No. Yes

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.

1 solution

Chan Lye Lee
Nov 8, 2018

Note that 11 1 19 times = k = 0 18 1 0 k \underbrace{11\ldots 1}_{19 \,\text{times}} = \sum_{k=0}^{18}10^k is a prime.

There is a conjecture that there are infinite many primes of the form 11 1 n times \underbrace{11\ldots 1}_{n \,\text{times}} .

Next prime is 111 11 23 times \underbrace{111\cdots 11}_{\text{23 times }} .

Naren Bhandari - 2 years, 7 months ago

Log in to reply

Values for n n such that those numbers are prime are

2 , 19 , 23 , 317 , 1031 , 49081 , 86453 , 109297 , 270343... 2, 19, 23, 317, 1031, 49081, 86453, 109297, 270343...

but only the first five are proven to be primes. The others are only "probable primes".

A Former Brilliant Member - 2 years, 7 months ago

Any proof for existence?

Vishwash Kumar ΓΞΩ - 1 year, 8 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...