Peter

A strange way to handle this. The provocation is OK, the reply not.

@AlexanderGruber Didn't you forget to delete something then ?

Last trial with my own PARI was a collection of more then 30 000 distinct "semisolutions". This problem is either very hard or has no solution which would however be a huge surprise since upto base 9 , there is at least one solution.

I ran even 6 windows with the online-tool , but soon they stopped. The speed is not very satisfying , also the 20 second limit (if no output comes) is bad. I hoped it would test primes much faster.

And 9N is in fact balanced. It seems we can find infinite many such primes.

Yes , I tested it also with this algorithm. I wonder whether it passes Miller Rabin with , say , the first 100 primes.

factordb

should be a prime number $N$ such that $9N$ is balanced. Please check !

((10^21560-1)*10^10*1234567890/(10^10-1)+4189257603)/9

I keep running my own PARI-tool.

seems to be the last output before the limited space for the output is exhausted

85317678304961095242

If someone can prove that there cannot be a solution , or has a useful criterion to sieve out the possible candidates , I would be very glad.

I begin to get exhausted by the exhaustive search ...

Important : To avoid duplicate effort , set a Seed with setrand (<any number>)

q=0;c=1;while(digits(c^3)<>g,gef=0;while(gef==0,a=random([1,20]);b=random([1,20]);h=v[a];v[a]=v[b];v[b]=h;s=vecsort(digits(fromdigits(v)^2));if(s==f,gef=1));c=fromdigits(v);if(vecsearch(x,c)==0,x=setunion(x,[c]);q=q+1;print(q," ",c," ",vecsort(digits(c^2))==f," ",vecsort(digits(c^3))==g)))

e=[];for(a=0,9,for(b=1,2,e=concat(e,a)));f=[];for(a=0,9,for(b=1,4,f=concat(f,a)));g=[];for(a=0,9,for(b=1,6,g=concat(g,a)));v=e;x=[]

Is someone wants to help here are the lines

At least 15 000 distinct solutions for N and N^2 do not satisfy the N^3-condition. Nevertheless , my guess is there is one solution based on the empirical probabilities , but it requires either much luck or much time to find one.

@Aurel-BG @MartinHopf I used the tool of Aurel (thanks!) AND simultaneously my own PARI/GP with a different approach (with many outputs , so that the tool does not stop unless I wait too long and the screensaver strikes). It is frustating. There are three possibilities 1. There is no solution 2. There is one , but it is like a needle in the heystack. 3. There are relative many solutions and I just had extreme bad luck to have not find one yet.

@SidvhidHsinynjad If you have PARI/GP , you can also join in the search. If not , you can download it and then join in.

@Aurel-BG Do you want to try another routine that might be better to find the solution ?

Merkwürdig ist auch , daß die Verbindung mit "factordb" als "unsicher" gilt. Wohl nur , weil ein Zertifikat nicht vorliegt. Dann kann man aber doch auf "factordb.com" klicken und wird weitergeleitet. Anscheinend ist dieser "Schutz" an sich ziemlich unzuverlässig. Mir erscheint "factordb" jedenfalls als absolut sicher.

@Aurel-BG

factordb

Is this a solution , or only a "semisolution" ?

OK, bye

OK, if you find a result , please output it here

factordb

I will try the primepi(10^12) again ...

and then it continues to run ?

20 seconds is not much ...

I quit "print(primepi(10^12))"

again quite high.

now an output ?

print(primepi(10^12)) seems to be somewhat slow

OK. Seems to work.

factordb

It is only a compiler , right ? I tried to enter "factor(24!-1)". How do I start it ?

seems it is not the one I used. Is it fast ?

please close/delete

or even better , delete the question

please delete this simply false answer

surely a duplicate , what is a suitable target ?

Despite the score , this should be deleted.

please delete

@SmokeDetector probably also "spam" , but flags for spam are usually declined.

this should be deleted despite its score. I know the suitable chatroom for this is CURED but there are too few users , so I try it here.

balanced-prime challenge also in progress

balanced-prime challenge also in progress