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Old 2019-02-06, 09:58   #1
enzocreti
 
Mar 2018

21216 Posts
Default Pg primes with exponent multiple of 201

The pg(k) numbers are formed by the concatenation of two consecutive Mersenne numbers...

pg(k)=(2^k-1)*10^d+2^(k-1)-1 where d is the number of decimal digits of 2^(k-1)-1

example pg(1)=10
pg(2)=31
pg(3)=73...


Consider when k is multiple of 201 and pg(k) is prime.
This happens for k=6231 and k=51456


6231/61 and 51456/61 will have the same 60 digit repeating term 147540...2131.
Why?
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Old 2019-02-06, 10:03   #2
axn
 
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Jun 2003

5,197 Posts
Default

Quote:
Originally Posted by enzocreti View Post
6231/61 and 51456/61 will have the same 60 digit repeating term 147540...2131.
Why?
What does 1/61 look like?

Last fiddled with by enzocreti on 2019-02-06 at 10:13
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Old 2019-02-06, 10:14   #3
enzocreti
 
Mar 2018

2·5·53 Posts
Default THE SAME?

the same?
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