Sequence Question

[henryzz]

Originally Posted by Brian-E

My guess is that a lot depends on how you implement the check of whether a number has been seen before. Obviously there are simple but very inefficient ways of doing this - and the most inefficient would take much more time than just following the chain to the end without the check. It's a non-trivial problem but I think if you try to optimize your method of checking for previous occurence you might dramatically improve the speed.

i am using a .net hashtable with the Numbers found being the keys
according to my dad who is a professional programer it is super quick

Originally Posted by petrw1

What I would do is create a boolean array.

Every time you get a number in the sequence check the array. If it is true you have a match. Otherwise turn it to true.

i think that would use too much memory cetainly if we are trying to get to something like 1e9
i would have to use a bitarray to try that method
i will try this tonight with booleans first and the slightly slower but lots less memory using bitarray

[robo_mojo]

Originally Posted by henryzz

i am using a .net hashtable with the Numbers found being the keys
according to my dad who is a professional programer it is super quick

But not as quick as using a direct bit-array, which wouldn't require hashing, but would require memory for each potential bit.

i think that would use too much memory cetainly if we are trying to get to something like 1e9
i would have to use a bitarray to try that method
i will try this tonight with booleans first and the slightly slower but lots less memory using bitarray

A boolean array is a bit array.

[henryzz]

Originally Posted by robo_mojo

A boolean array is a bit array.

not in .net
the diferences are:
bitArrays uses a huge amount less memory(i have experience of this)
when debuging u cant view the values of a bitArray but u can with booleans

it is possible to just change the declaration and it will work so debugging and memory are the only diffences

[robo_mojo]

Originally Posted by henryzz

not in .net
the diferences are:
bitArrays uses a huge amount less memory(i have experience of this)
when debuging u cant view the values of a bitArray but u can with booleans

it is possible to just change the declaration and it will work so debugging and memory are the only diffences

What I meant was when petrw1 said "boolean array" he probably meant the same thing that you call a bit array. A bit array stores only one bit per value, and can be searched in constant time.

[petrw1]

Originally Posted by robo_mojo

What I meant was when petrw1 said "boolean array" he probably meant the same thing that you call a bit array. A bit array stores only one bit per value, and can be searched in constant time.

Exactly, without getting into programming language semantics I simply meant a structure where each bit represents Y or N (has the corresponding number shown up yet...or has it not.)

[nfortino]

Personally, I wouldn't bother with the bit array at all, but rather just stop checking once a number smaller than I started with is reached. If you start at 3 and go up, you are assured to be correct (in small tests this gives a speed up of a factor of ~5). Also, only bother checking with starting primes of the form 6k - 1, as primes of the form 6k +1 go straight back to a number bounded by 4k + 1 in two steps. Since this is really a question about Sophie Germain primes and Cunningham chains, any knowledge from there would apply directly here.

[henryzz]

[quote=nfortino;132429]Personally, I wouldn't bother with the bit array at all, but rather just stop checking once a number smaller than I started with is reached. quote]
i am already doing that

Originally Posted by nfortino

Also, only bother checking with starting primes of the form 6k - 1, as primes of the form 6k +1 go straight back to a number bounded by 4k + 1 in two steps.

i will try this later it should speed it up lots


i am in the process of speeding up the factoring and that seems to be using most of the time so that may help a lot

[henryzz]

Originally Posted by nfortino

Also, only bother checking with starting primes of the form 6k - 1, as primes of the form 6k +1 go straight back to a number bounded by 4k + 1 in two steps. Since this is really a question about Sophie Germain primes and Cunningham chains, any knowledge from there would apply directly here.

i dont understand why having a number of form 4k+1 means that it is not possible for that sequence to not eventurally become 3
also what is wrong with 5k-1 for example

[Brian-E]

Originally Posted by henryzz

i dont understand why having a number of form 4k+1 means that it is not possible for that sequence to not eventurally become 3
also what is wrong with 5k-1 for example

The point is that numbers of the form 6k+1 reduce to a lower number in only two steps which, according to nfortino's method, means that you don't need to follow these chains any further.

Nothing is wrong with numbers of the form 5k-1, but nfortino is suggesting that you specifically consider the numbers modulo 6 because only the case of 5 mod 6 needs to be checked each time.

[henryzz]

Originally Posted by Brian-E

The point is that numbers of the form 6k+1 reduce to a lower number in only two steps which, according to nfortino's method [which you say you were already implementing in which case I can't understand why you were using bit arrays at all], means that you don't need to follow these chains any further.

Nothing is wrong with numbers of the form 5k-1, but nfortino is suggesting that you specifically consider the numbers modulo 6 because only the case of 5 mod 6 needs to be checked each time.

thanks
i have taken it to 50mil and i am gonna look for other methods of finding a solution