20181214, 13:20  #45 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 
All a coincidence is, is two things happening together, usually without apparent cause or connection.
So by saying these things aren't coincidences you are implying there is a connection, or cause. But you are unwilling to make a proof (not unable I might add). Math is more rigorous than your statements. Math forces you to start from a set of definitions and axioms, and use a set of rules of inferences to show in a given logic setup, that your statement not being true is impossible. here are a few properties of the superset the set you are interested must follow:

20181214, 16:17  #46 
Aug 2006
3×1,987 Posts 
You weren't able to find the probability for the simplified model of my simplified model. What makes you so sure that you can determine the likelihood for the much more complicated case all in your head, without any supporting calculations? (Does anyone else in the thread have so much hubris?)
I think you should seriously look at post #21 by VBCurtis. It's good advice, if posted somewhat abrasively. 
20181215, 07:47  #47 
Mar 2018
20F_{16} Posts 
Sloane
In a email Sloane told me that these numbers are not random at all!

20181215, 16:32  #48 
Mar 2018
17×31 Posts 
Look at this "coincidence"
pg(43k) is prime in the cases:
pg(215), pg(69660), pg(92020) and pg(541456) (215111)/13+35=43. (69660+111)/1335=2^2*31*43 (92020+111)/1335=2^2*41*43 (541456+111)/1335=2^3*11^2*43. 
20181215, 17:01  #49  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2430_{16} Posts 
Quote:
No, you just didn't understand what he wrote (*). Consider this: does Sloane collect truly random sequences? No  he would have run out of all disks in the world if he did. Therefore  sequences in his database are not random. _____________ * This is how the Korean Godfather solves problems: "I made them an offer that they couldn't understand" 

20181215, 17:17  #50 
Mar 2018
17×31 Posts 
Pattern
when k is a multiple of 43, it seems that pg(k), when it is prime (or probable prime), follows a pattern!

20181215, 18:52  #51 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 

20181215, 18:53  #52 
Mar 2018
17·31 Posts 
pg(67k) primes
the probable primes pg(67k) are pg(67) and pg(51456)...67 and 51456 are both 2 mod 13

20181215, 19:15  #53  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{4}×3×193 Posts 
Quote:


20181216, 07:08  #54 
Mar 2018
17·31 Posts 
example
could you please give me an example of the patterns you found?

20181216, 08:57  #55  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{4}·3·193 Posts 
Quote:
Here is one pattern for you to start: 31 is prime 331 is prime 3331 is prime 33331 is prime 333331 is prime 3333331 is prime 33333331 is prime Is 333...331 always prime?? (This is example 6 from R.K.Guy's famous paper.) 

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