20181211, 08:28  #1 
Mar 2018
2×5×53 Posts 
541456 and 51456. I checked 20 numbers 2000 times and found 200 patterns!!
pg(k)=M(k)M(k1) where  denotes concatenation base 10 and M(k) is the kth Mersenne number. Examples of such numbers are 1023511, 255127, 12763...
I found that pg(k) is prime for k=51456 and for k=541456. I wonder if that is only a coincidence (54145651456=700^2) or there is an hidden structure undermeath these numbers. What is the probability to have by mere chance two probable primes with these two amazing exponents? 
20181211, 09:08  #2  
Jun 2003
2×3×7×11^{2} Posts 
Yes, unfortunately.
Quote:
As such, what you're doing is looking for afterthefact coincidences. When you started out with this series, you were only focusing on the lack of 6 (mod 7) primes. Now you're focusing on pairs of "amazing" exponents. But none of these were predicted beforehand. You just looked at the numbers (which gives primes) and tried to find coincidences, and you did. Nothing more. 

20181211, 09:14  #3  
Mar 2018
212_{16} Posts 
IT IS NOT A COINCIDENCE!
Quote:
I am sure it is NOT a coincidence!!! 

20181211, 09:18  #4 
Mar 2018
2×5×53 Posts 
pg(2131) and pg(2131*9=19179)
also this is a coincidence: pg(2131) is prime and pg(2131*9) is prime!!!

20181211, 11:04  #5 
Jun 2003
2·3·7·11^{2} Posts 
I understand that you think these are not coincidences. You will keep on trying to find "hidden patterns". I have said all I can. Good luck.

20181211, 16:49  #6  
"Curtis"
Feb 2005
Riverside, CA
1001100000100_{2} Posts 
Quote:
You have no idea what you mean what you say "this is not a coincidence," and it makes you look like a fool. You're practicing the primenumber version of throwing darts at a dartboard, and then expressing amazement that you can find some meaning in the score. Perhaps you have a knack for astrology; those people find meaning in trivial happenings too. 

20181211, 17:47  #7  
Aug 2006
13533_{8} Posts 
Quote:
Quote:
pg(36) is prime, and so is pg(36*1935). pg(67) is prime, and so is pg(67*93). pg(67) is prime, and so is pg(67*768). pg(215) is prime, and so is pg(215*324). pg(215) is prime, and so is pg(215*428). I discarded the numbers under 36 (to avoid getting easy small multiples) and 541456 (because it wasn't clear if some numbers were skipped). This is far more than the number of multiples expected by chance. Does this suggest that multiples of earlier terms are more likely, or just that having small factors are more likely? It's not clear to me. Last fiddled with by CRGreathouse on 20181211 at 17:57 

20181211, 18:18  #8 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
22426_{8} Posts 

20181211, 18:39  #9 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 
are all multiples that work for larger values multiples of 3?
Last fiddled with by science_man_88 on 20181211 at 18:48 
20181212, 07:09  #10  
Mar 2018
1000010010_{2} Posts 
Primes
Quote:
I don't know, the only thing I can see is that these numbers are not random at all! 

20181212, 17:18  #11  
Mar 2018
2·5·53 Posts 
WHO ARE YOU?
Quote:


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