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   Author  Topic: prime number with all digits equal  (Read 253 times)
gkwal
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prime number with all digits equal  
« on: Jul 16th, 2007, 9:36pm »		 Quote Quote Modify Modify
Which numbers whose digits are all equal are prime?
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jollytall
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Re: prime number with all digits equal  
« Reply #1 on: Jul 17th, 2007, 1:06am »		 Quote Quote Modify Modify
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.
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towr
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Re: prime number with all digits equal  
« Reply #2 on: Jul 17th, 2007, 1:53am »		 Quote Quote Modify Modify
http://www.research.att.com/~njas/sequences/A116692
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Wikipedia, Google, Mathworld, Integer sequence DB
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