mersenneforum.org Digitally delicate prime numbers
 Register FAQ Search Today's Posts Mark Forums Read

2021-04-06, 00:27   #1
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

2·1,009 Posts
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

 2021-04-06, 01:09 #2 VBCurtis     "Curtis" Feb 2005 Riverside, CA 477910 Posts 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.
 2021-04-06, 02:00 #3 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 201810 Posts I assume the 1st such a prime discovered would qualify for both of the remaining EFF Awards.
 2021-04-06, 02:34 #4 LaurV Romulan Interpreter     Jun 2011 Thailand 5·1,889 Posts 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...
 2021-04-06, 02:41 #5 axn     Jun 2003 2×3×827 Posts
2021-04-06, 03:32   #6
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

2×1,009 Posts

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.

Last fiddled with by a1call on 2021-04-06 at 04:06

 2021-04-06, 04:31 #7 LaurV Romulan Interpreter     Jun 2011 Thailand 5×1,889 Posts 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).
 2021-04-06, 04:40 #8 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2·1,009 Posts 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.
 2021-04-06, 05:13 #9 axn     Jun 2003 2×3×827 Posts Are you thinking that the number must have that property in _all_ the bases simultaneously?
 2021-04-06, 05:19 #10 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 7E216 Posts 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? Last fiddled with by a1call on 2021-04-06 at 05:20
 2021-04-06, 05:22 #11 axn     Jun 2003 2·3·827 Posts RTFA. Stop projecting your wishes on to what was actually done.

 Similar Threads Thread Thread Starter Forum Replies Last Post dabaichi News 571 2020-10-26 11:02 pepi37 Information & Answers 2 2015-05-21 20:50 kgr Miscellaneous Math 3 2013-03-04 09:20 mfgoode Lounge 5 2007-08-15 16:53 Frodo42 Lounge 1 2005-06-15 19:44

All times are UTC. The time now is 03:21.

Wed May 12 03:21:08 UTC 2021 up 33 days, 22:02, 0 users, load averages: 1.43, 1.62, 1.56