wu :: forums - Print Page


    
      
        wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> medium >> prime number with all digits equal
        
(Message started by: gkwal on Jul 16^th, 2007, 9:36pm)

Title: prime number with all digits equal
Post by gkwal on Jul 16^th, 2007, 9:36pm

Which numbers whose digits are all equal are prime?

Title: Re: prime number with all digits equal
Post by jollytall on Jul 17^th, 2007, 1:06am

Few thoughts:

Single digit primes: OK.
All others by digit:
0, not a multi-digit number.
d>1, all dividable by d.
So it must be in the form 1....1.

The number of digits:
2: OK. 11.
2k, k>1: not OK, dividable by 11.
3k: Not OK, dividable by 3.
So, only possible 6k +/- 1.

But from thereon, I am not sure, whether can be easily further limited. The next prime is:
1111111111111111111, but there can be many more.

Title: Re: prime number with all digits equal
Post by towr on Jul 17^th, 2007, 1:53am

http://www.research.att.com/~njas/sequences/A116692