20141205, 09:17  #1 
"M49"
Dec 2014
Austria
2^{3}×3 Posts 
Is there a primality test for Repunits? I am too lazy to read...
..... and if u really wanna help me, please provide more info than "Read Knuth´s book" a la RDS ...
To be more specific, we are dealing with numbers of the form (10^n1)/9 thanks Last fiddled with by ProximaCentauri on 20141205 at 09:22 
20141205, 09:39  #2 
"M49"
Dec 2014
Austria
2^{3}×3 Posts 
Hi Supermod,
Do u find it fair to edit the title after posted? Who do you think you are? 
20141205, 10:02  #3 
"Brian"
Jul 2007
The Netherlands
7×467 Posts 
If you google "repunit prime" you see the answer to your question and lots of other information.

20141205, 11:23  #4  
May 2004
New York City
2^{3}·23^{2} Posts 
Quote:
There are others. At least one other. BTW 1 is not prime, and 2 is prime, so my rule has the exception: 11 is prime. 

20141205, 13:06  #5 
"M49"
Dec 2014
Austria
2^{3}·3 Posts 
ya thanks I am fully aware of this, but still searching for a primality test available, maybe LLlike with Lucas sequences.
Is there a program which can perform such a primality test on RepUnits? I still did not find. Last fiddled with by ProximaCentauri on 20141205 at 13:26 
20141205, 15:54  #6 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
There's nothing so simple as the LL test. If there were, we would not find repunit primes on the PRP Top list. Some generalized repunit primes are proven via N1 factoring. This is because N1's factorization is related to the factors of some numbers of the form 10^n+1. For example, where R(n) = (10^n1)/9
R(270343) is PRP. 270342 = 2 * 3^2 * 23 * 653 R(270343)1 is divisible by 10^653+1 R(270343)1 is divisible by 10^(3*653)+1 etc. So if n is smooth, it will be easier to find some factors of N1. If you can factor 33.33% of N1, you can run an N1 primality test. 
20141205, 16:43  #7  
"M49"
Dec 2014
Austria
2^{3}·3 Posts 
Quote:


20141205, 18:02  #8  
May 2013
East. Always East.
11·157 Posts 
Quote:
In this case you've made yourself a big target by being extra specific about not being told to go read a book. If you'd simply asked "Does anyone know if there is a primality test for numbers of the form 1/9 * (10^{n}  1)?" you may not have been trolled quite as hard. Now I am giving you some asofyet unwarranted credit by assuming you DID do some searching around first. It takes less time and fewer keyboard presses to just Google Repunit Primality Test and look at what comes up. To your credit, such a Test does not appear so your question is valid in that sense as a "Does Anyone Happen to Know of One?" blurb. Last fiddled with by TheMawn on 20141205 at 18:03 

20141205, 18:23  #9 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
10253_{8} Posts 

20141205, 19:06  #10  
"M49"
Dec 2014
Austria
24_{10} Posts 
Quote:
Yeah I did research before, such as Code:
Irish Math. Soc. Bulletin 59 (2007), 29–35 29 Factoring Generalized Repunits JOHN H. JAROMA They seem to be very rare in base 10, maybe even less dense than the Mersenne Primes. However, Lucas sequences are involved similar like in LLRtests. Harvey Dubner stated that R49081 is a PRP in March 2001 and he also said the only chance of proving it prime with current theory and technology is using the BLS method. This requires that (R49081 − 1) be about 1/3 factored, that is, the product of the known prime factors of (R49081 − 1) should be about (R49081 − 1)^{3}. Thx mawn for your credit, even unwarranted 

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