[HN Gopher] Mathematicians Find a New Class of Digitally Delicat...
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Mathematicians Find a New Class of Digitally Delicate Primes
Author : susam
Score : 75 points
Date : 2021-03-31 05:24 UTC (1 days ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| ram_rar wrote:
| I am wondering, what kind of implications will it have on
| encryption. Would it be easier to break down prime factorization
| if they are composed of digitally delicate primes?
| jerf wrote:
| I would expect it to be irrelevant. If being able to factor
| slightly different numbers was very helpful in factoring a
| particular number it would already be something we can do;
| generating known-factorable numbers from a prime is trivial.
| MaxBarraclough wrote:
| > Here, his sweatshirt lists the first 20 digitally delicate
| primes.
|
| Isn't the first digitally delicate prime simply 2? Or are single-
| digit primes excluded? Or am I missing something terribly
| fundamental?
|
| _edit_ Or is it that, because we can replace 2 by 3 and still
| get a prime, it doesn 't count? Which is to say, replacing any
| digit in the number by _any_ other digit, must always result in a
| non-prime?
| paul_f wrote:
| Yes, you can change the 2 to a 3 and it is still prime. So 2 is
| not digitally delicate
| MaxBarraclough wrote:
| Thanks. The article could have been more explicit on this
| point.
| kzrdude wrote:
| I'm surprised that "digitally delicate primes" are rare, why
| isn't this the majority of primes? That would be my intuition.
| qsort wrote:
| For a prime to be delicate as per the definition given, all
| numbers with "levhensthein distance" 1 must be composite. This
| puts a lot of conditions on what the prime can be, for p = a_0
| + a_1 b + a_2 b^2 + ... + a_n b^n, if p is delicate then (p -
| a_0), (p - a_0 + 1), ..., (p - a_0 + b - 1) must all be
| composite, and so must be (p - b a_1), ..., (p - b a_1 + b
| (b-1)), and so forth.
|
| This is equivalent to proving that certain slices of some
| arithmetic successions contain no primes. Not a professional
| mathematician and I didn't read the paper, but I suspect this
| is related to prime gaps works by Tao, who is cited in the
| article.
| breck wrote:
| This is a great explanation, thanks!
| dnautics wrote:
| You must be able to change _any_ digit into _any_ other digit.
| Zenst wrote:
| Now if somebody asks for a large prime number safe from bit
| errors I will know the answer.
| aritmo wrote:
| Not much they "found" but rather they "declared" a new class.
| gweinberg wrote:
| Whether math is discovered or invented is always open to
| debate.
| lupire wrote:
| You might have overlooked the first sentence of the article:
|
| > Despite finding no specific examples,
| thewakalix wrote:
| That's a matter of philosophical disagreement (ferex,
| Platonism).
| lupire wrote:
| https://news.ycombinator.com/item?id=26667203
| neallindsay wrote:
| I love a good math article where "digital" means "base 10".
| bugzz wrote:
| It's a property referencing the digits - thus "digital". The
| results hold for all bases, not just base 10.
| patrec wrote:
| Digit = finger. Most people have 10. It was a pun.
| gibolt wrote:
| I have a 2 handed phone number
| lupire wrote:
| Every base is base 10.
| ABeeSea wrote:
| Primes are the same irrespective of base...
| enchiridion wrote:
| Is this true for digitally delicate primes as well?
| aardvark179 wrote:
| Different primes will be delicate in different bases (you
| can trivially demonstrate this by considering a prime n in
| base n-1) but they exist in all bases.
| [deleted]
| DannyB2 wrote:
| A prime might be 'delicate' in base 10 but not be delicate in
| base 8.
|
| Another prime might NOT be delicate in base 10 but be
| delicate in base 8.
| ABeeSea wrote:
| Right that's explained in the article. I assumed OP only
| read the headline and assumed "digital" meant binary rather
| than an actual digit.
| booleandilemma wrote:
| Wouldn't it be more interesting to find a prime number where
| changing any single digit (maybe besides the least significant
| one) would still be a prime? Call it a sturdy prime.
| qsort wrote:
| No such numbers except a small number of trivial cases exist.
| In odd bases, n % 2 === (sum of the digits of n), and in even
| bases, n % (b-1) === (sum of the digits of n).
| kosievdmerwe wrote:
| If we weaken the condition, to allow you to choose the
| replacement digit there are definitely semi-sturdy primes.
|
| For instance, 23 is semi-sturdy as you can replace 2 by 1 or
| 3 by 9 and both 13 and 29 are prime.
|
| The interesting question then becomes: how many?
| [deleted]
| f154hfds wrote:
| Well you all heard the challenge. Who has got idle GPUs sitting
| around? Let's find the smallest base 10 widely digitally delicate
| prime!
|
| In all seriousness though, it's fascinating that we know this
| number exists but have no idea what it is. What a treasure hunt..
| kemiller wrote:
| Missed opportunity to call them "digital delicacies".
| nullsense wrote:
| Nice.
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