mersenneforum.org 541456 and 51456. I checked 20 numbers 2000 times and found 200 patterns!!
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 2018-12-16, 10:54 #56 enzocreti   Mar 2018 52710 Posts Example Naaaaaaaaa...that's a bad example
 2018-12-16, 11:09 #57 enzocreti   Mar 2018 17×31 Posts Pg(k) Primes of this form follow a rule...the only problem is that there yet too few many primes found and the rule is so difficult that only a top mathematician could find it
2018-12-16, 13:03   #58
Dr Sardonicus

Feb 2017
Nowhere

25·7·17 Posts

Quote:
 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!
Quote:
 Every crime has its own pattern of logic. Everything has an order. If we cannot find that order, it's not because it doesn't exist... but because we have incorrectly examined s-s-some vital piece of evidence. Let us examine the evidence. Number one: In the past six months, there have been 345 homicides committed in this city. The victims have ranged various-s-sly in age... sex, social status and-and color. Number two: In none of these homicides have we been able to find the motive. Number three: Consequently, all 345 homicides remain unsolved. So much for the evidence. A subtle pattern begins to emerge. What is this pattern? What is it that these 345 homicides... have-have-have, uh-uh-uh... have in common? They... They have in common three things: A: They have nothing in common: B: They have no motive: And C: They remain unsolved.
-- Lieutenent Practice, Little Murders (1971)

2018-12-16, 16:03   #59
CRGreathouse

Aug 2006

2×2,969 Posts

Quote:
 Originally Posted by enzocreti Primes of this form follow a rule...the only problem is that there yet too few many primes found and the rule is so difficult that only a top mathematician could find it
Do you have any evidence supporting this bold assertion?

2018-12-16, 16:49   #60
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

8,369 Posts

Quote:
 Originally Posted by enzocreti Primes of this form follow a rule...the only problem is that there yet too few many primes found and the rule is so difficult that only a top mathematician could find it
I still think the Strong law of Small numbers applies:

if the exponent d was more regular, you'd expect such runs. it just happens regular for long stretches

 2018-12-16, 16:56 #61 enzocreti   Mar 2018 17×31 Posts THE ACE Now i think i will drop the ace: pg(215), pg(69660) and pg(92020) are probable primes (215,69660,92020 are multiples of 215). Amazingly pg(215), pg(69660) and pg(92020) are all congruent to 15 mod 31!!!
2018-12-16, 17:22   #62
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

23·5·229 Posts

Quote:
 Originally Posted by enzocreti Naaaaaaaaa...that's a bad example
Tigger is introduced in Chapter II of House at Pooh Corner, when he arrives at Winnie-the-Pooh's doorstep in the middle of the night, announcing himself with a stylised roar.

Most of the rest of that chapter is taken up with the characters' search for a food that Tigger can eat for breakfast — despite Tigger's claims to like "everything," it is quickly proven he does not like honey, acorns, thistles, or most of the contents of Kanga's larder.

 2018-12-16, 19:43 #63 enzocreti   Mar 2018 17·31 Posts pk(215k) all pg(215k)'s are congruent to 15 mod 31!
2018-12-16, 19:57   #64
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

23·5·229 Posts

Quote:
 Originally Posted by enzocreti all pg(215k)'s are congruent to 15 mod 31!
Stop being silly. 215k is divisible by 5.
All pg(m) are congruent to 15 mod 31 when 5|m -- which is entirely obvious.

That's some ace you got. "Three values that could not be anything but 15 mod 31, turned out to be 15 mod 31. Oh the shock!"

 2018-12-16, 22:37 #65 JM Montolio A   Feb 2018 1408 Posts The prime numbers dont follows any rule. They are the small few survivors after all the rules applied. At infinite only the gap fills the black space, and they looks like lonely stars.
 2018-12-17, 08:34 #66 enzocreti   Mar 2018 17·31 Posts pg(69660), pg(92020), pg(541456) pg(69660), pg(92020) and pg(541456) are probbale primes and they are all congruent to 7 mod 10. So it seems that when pg(86k) is prime, then it is congruent to 7 mod 10!

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