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Primes'

What does this mean ?
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the following is a set of numbers fitting a particular pattern in the set of prime numbers that I have stumbled upon sometime ago.

for n >= 1

for each Prime p such that 10^n < p < 10^(n+1) // 10..100, 100..1000, ...etc

for x = 10^(n+1) - (p - 10^n)

check if x is prime. // for n = 1 it yields 13,31,37,43,67,73,79,97

that's all, the idea was to focus on a set of primes based of the number of digits it is comprised of.

latte, Jun 26 2020

Goldbach‘s Conjecture https://en.wikipedi...bach%27s_conjecture
Every even integer greater than 2 can be expressed as the sum of two primes. [kdf, Jun 27 2020]

[link]






       Is this a theorem? A puzzle? An idea for an invention (poorly thought out or otherwise)?
kdf, Jun 26 2020
  

       Please describe the theory you're presenting.
Voice, Jun 26 2020
  

       10^(n+1) - (p - 10^n) is not a very elegantly written expression.
pocmloc, Jun 26 2020
  

       Welcome to the HB [latte]
Could you take the time and trouble to rephrase your "idea" so that it becomes an actual idea? eg "idea for a mathematical formula that quickly and easily determines if a number is prime based on a count of its digits"
  

       You then outline the halfbaked method of acheiving the outcome you have outlined. The emphasis here is on it being halfbaked, otherwise it's not by definition a halfbaked idea!
Meanwhile, have this croissant [+] to cancel out the bone someone sent you as a welcoming gift. No new member should start off here with a bone (my first post attracted 6 bones so I know how it feels)
xenzag, Jun 26 2020
  

       Mine only collected 4 ; your post must have been much crappier.
FlyingToaster, Jun 26 2020
  

       [kdf] [Voice] that is what I want to find out, I was exploring links between prime numbers within logarithmic upper and lower bounds and then I noticed this 100 - 3 = 97, 100 - 87 = 13 (97 - 10 = 87 & 13 - 10 = 3), then the flipping between digit symbols 13 to 31 & 37 to 73 & 79 to 97 with 43 & 67 being the odd ones out (original post had 41 & 59, sorry). I don't know what it means, I've been seeking feedback....   

       [pocmloc] you should have seen the haskell line that does the same thing, I don't remember it, it's been a while.   

       [xenzag] Thank you, I had a pain au chocolat this morning every bite dipped in coffee...   

       Has anybody seen this before ?   

       Sorry for the late reply, I'm still getting to know the UI.
latte, Jun 26 2020
  

       Welcome, [latte]. I'm not sure what this idea means, but the attempt to understand it woke up my brain on a slow morning so you've done me a favour already. [+]
pertinax, Jun 27 2020
  

       i don’t know if it “means” anything. But it might help you to look up some existing theorems and conjectures about primes - you might be reviewing something already known.   

       Start with Goldbach’s conjecture (link) which posits every even integer greater than 2 can be expressed as the sum of two primes. It doesn’t touch on everything you mentioned - but it’s no surprise you can subtract a prime from 100, or 1000, etc and have a prime left over.
kdf, Jun 27 2020
  

       i don’t know if it “means” anything. But it look up some existing theorems and conjectures about primes - you might be reviewing something already known. Start with Goldbach’s conjecture (link) ... It doesn’t touch on everything you mentioned - but it’s no surprise you can subtract a prime from 100, or 1000, etc and have a prime left over.
kdf, Jun 27 2020
  

       [latte] you still have time to change your flight to a saner, nicer, busier, cooler site.   

       Cause once your plane leaves the runway, you are ours for good.
blissmiss, Jun 27 2020
  

       //subtract a prime from 100, or 1000, etc and have a prime left over// But the example given subtracts a prime from 110 to have a prime left over.   

       Is there something special about 1.1 x 10^n or could we chose any random number and subtract primes from it?
pocmloc, Jun 27 2020
  

       pocmloc - not just any prime. There are some pairs of primes that add up to 100, but 100-(some prime) does not always leave (some other prime). -   

       That may be part what latte was going on about. His complete idea wasn’t clear to me ... but any discussion of special classes of numbers usually makes me eyes glaze over pretty quickly.
kdf, Jun 27 2020
  

       I think the thing to do would be to work out whether there was an excess of 'paired primes' over that expected by chance.
So you'd choose a range - I think preferably not overlapping with its mapping. Then you can determine the number of paired primes, divide this by the number of primes present in the range, and compare that to the fraction of numbers in the mapped range which are prime.
  

       I preliminarily did this for n=1, and did see a small excess - which didn't look particularly convincing (also it was very late at night; E&OE). To interest a mathematician I think you'd need to show there was a consistent trend.
Easy route would use a short program and a list of primes found on the internet - I found a reasonably formatted list of the first 100,000 with a little searching, so that's doable.
Loris, Jun 28 2020
  

       I think you should look at the patterns produced using other number bases. The use of base 10 is embedded within your formula, yet prime numbers have no number base bias.
Lemon, Jun 28 2020
  

       Lemon...LEMON...Get over here and let me squeeze you. Hahaha Good to see an old face.
blissmiss, Jun 28 2020
  

       Hiya blissmiss, and Po who said hello when I popped up a few weeks ago. Good to see so many old faces are still here.
Lemon, Jun 30 2020
  
      
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