541456 and 51456. I checked 20 numbers 2000 times and found 200 patterns!!

[science_man_88]

Originally Posted by enzocreti

If all these are coincidences, I am superman!

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:

1. no divisor other than 2 or 5 divides n for concat(2n+1,n)
2. no divisor other than 2 or 5 divides 2n+1 for concat(2n+1,n)
3. the sum of digits will be 1 mod 3.

[CRGreathouse]

Originally Posted by enzocreti

If all these are coincidences, I am superman!

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.

[enzocreti]

In a email Sloane told me that these numbers are not random at all!

[enzocreti]

pg(43k) is prime in the cases:

pg(215), pg(69660), pg(92020) and pg(541456)


(215-111)/13+35=43.

(69660+111)/13-35=2^2*31*43

(92020+111)/13-35=2^2*41*43

(541456+111)/13-35=2^3*11^2*43.

[Batalov]

Originally Posted by enzocreti

In a email Sloane told me that these numbers are not random at all!

Proof by authority at its best!

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"

[enzocreti]

when k is a multiple of 43, it seems that pg(k), when it is prime (or probable prime), follows a pattern!

[science_man_88]

Originally Posted by enzocreti

when k is a multiple of 43, it seems that pg(k), when it is prime (or probable prime), follows a pattern!

what remainders do mersennes have mod 43 ?

[enzocreti]

the probable primes pg(67k) are pg(67) and pg(51456)...67 and 51456 are both 2 mod 13

[Batalov]

'Learn, learn, and learn!' (V.I.Lenin)

Read this and process it mentally - https://en.wikipedia.org/wiki/Multip...risons_problem

[enzocreti]

could you please give me an example of the patterns you found?

[Batalov]

Originally Posted by enzocreti

could you please give me an example of the patterns you found?

You appear to be unable to distinguish patterns from noise, so you would not be able to see them. You have to learn first.

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.)