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Old 2021-04-06, 00:27   #1
a1call
 
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Default Digitally delicate prime numbers

Didn't see this posted anywhere:

Quote:
Digitally delicate prime numbers become composite with this one weird trick.
Math researchers proved these primes exist using the bucket proof method.
There are no known examples so far, but mathematicians are hopeful.
https://www.popularmechanics.com/sci...-prime-number/

I holes it's not an April-Fools article.

Last fiddled with by retina on 2021-04-06 at 04:51 Reason: Title is now more meaningful and less vague
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Old 2021-04-06, 01:09   #2
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I'm sad you managed to find someone who used "one weird trick" clickbait for an actual math discovery.

Give quantamagazine.org a try for a better article on the research.
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Old 2021-04-06, 02:00   #3
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I assume the 1st such a prime discovered would qualify for both of the remaining EFF Awards.
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Old 2021-04-06, 02:34   #4
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How did you come to that assumption? As I understand, they only searched to 10^9, so the first found may have as low as 10 digits. Which I personally doubt, but numbers are clever, they may surprise you...
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Old 2021-04-06, 02:41   #5
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https://www.mersenneforum.org/showth...009#post575009
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Old 2021-04-06, 03:32   #6
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Quote:
In new research, mathematicians have revealed a new category of “digitally delicate” prime numbers. These infinitely long primes turn back to composites faster than Cinderella at midnight with a change of any individual digit.
* I assume this would rule out any such prime being a twin prime.
* If there are infinite twin primes (or any other Even-number-separated-primes) then there have to be other types of infinitely-digited primes that do not turn into composites by changing a single digit.

ETA Unless, while infinitely numerous, none of the twin primes have infinite number of digits.

ETA Ii which would bring up the possibility of existence of a new relationship where infinitely-digited primes separated by some given/constant infinitely-digited number may be infinitely numerous.

ETA Iii Which raises the question: Would an infinitely-Digited integer written in the base m, where m is another infinitely-digited-integer have limited number of digits? If so would they still behave like Cinderella in such bases?

ETA IV I foresee a sleepiness night. Hey Google, cancel all my meetings for tomorrow.

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Old 2021-04-06, 04:31   #7
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Again, how did you get the conclusion that such prime has an "infinite number of digits"?(which is an aberration it itself, you can not say that an integer, prime or not, has an infinite number of digits). They talk about a fix number, which can have as low as 10 digits, in front of which they add an infinite number of zeros. But the prime is finite, it has a finite number of digits.

This prime can be a twin prime (why not? think 59 and 61, you cannot transform one to another by flipping a single digit).
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Old 2021-04-06, 04:40   #8
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Let p be any prime greater than 2*11.
Let b=p-11
then,
p can always be written as
p=1:11b
as a 2 digit number in base b.
Changing the 1st digit to 0 will not make it behave like Cinderella. It will always give a prime number, 11.
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Old 2021-04-06, 05:13   #9
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Are you thinking that the number must have that property in _all_ the bases simultaneously?
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Old 2021-04-06, 05:19   #10
a1call
 
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Obviously not in integer bases with infinite digits.
What bases/base would that number be a Cinderella in? Base 10 only?
Wouldn't that be too arbitrary? Just because we have 10 toes?

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Old 2021-04-06, 05:22   #11
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RTFA. Stop projecting your wishes on to what was actually done.
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