Question

thinking about this question ,if anyone have idea
http://openstudy.com/study#/updates/53ee042fe4b0f30a87d63d4d

Answer 1

@Kainui
also this we need to think about

Answer 2

we need to find some common composite property for these only

34343
34343434343
34343434343434343
34343434343434343434343
34343434343434343434343434343

Answer 3

lets not consider other two cases which are already proven

Answer 4

well if any one find anything i'll be online soon
just type it

Answer 5

if u mean that what is the pattern of that equation consider that:
\( \large \Large a _{n} = 10^{6} a _{n-1} + 434343\)

and of \(\large a _{n} = pa _{n-1} + q\) and \( \large a_{1} = r \) then,

\[\large a _{n} = rp ^{n-1} + q.\frac{ p^{n-1} -1}{ p-1 }\]
(i can prove it... if u want,i'll prove it in a new question)

Answer 6

so here,in this sequence we have:

\[\Large a _{n} = 34343(10^{6n-6}) + 434343(\frac{ 10^{6n-6}-1 }{ 10^{6}-1 })\]

Answer 7

u meant this?

Answer 8

na i know the pattern i want to prove why its composite each time

Answer 9

wel,then got it :)

Answer 10

k , how ? :D

Answer 11

i'm trying to use that pattern and show that all of them are composite.

Answer 12

ok have fun :P
but note that we have prove 2 part in the sequence
this pattern is not proven yet
34343
34343434343
34343434343434343
34343434343434343434343
34343434343434343434343434343

Answer 13

ok let me read those proofs carefully,maybe i get some idea...

Answer 14

when number of digits lets say n
and n mod 3=2

Answer 15

not getting idea...
i'll be back for about 2 hours.have u got any idea?

Answer 16

no i have reached up to
400 digit :D no prime

Answer 17

just change interval >.<
http://www.wolframalpha.com/input/?i=table+of+primeQ%2834343*%2810%5E%286n%E2%88%926%29%29%2B434343*%28%2810%5E%286n%E2%88%926%29%E2%88%921%29%2F%2810%5E6%E2%88%921%29%29%29+for+n+%3D+350+to+380

Answer 18

:D
don't do that any more,now we are confident that there's no prime.let just prove it...i'm trying to write the numbers in a way which can prove that all of them are composite...