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From Sharon Lourduraj <sharon.lourdu...@gmail.com>
Subject Re: [math] Prime Numbers Library.
Date Sat, 11 Mar 2006 19:28:51 GMT
```All right then, I will start by creating a Wiki entry in the Math Wish
list. And proceed form there on.

Thanks,
Sharon

Phil Steitz wrote:
> On 3/11/06, Sharon Lourduraj <sharon.lourduraj@gmail.com> wrote:
>
>> Hello Phil,
>>
>> Prime Number Theory is a huge subject. To start of with we can focus on
>> implementing prime finding methods, such as divide by odd numbers up to
>> the square root of a number, divide by primes up to the square root of a
>> number and Sieve of Eratosthenes. As we move along, we can implement
>> prime finding of specific types, Mersenne Prime, Twin Primes,
>> Palindromic Primes etc. And as we move along with those implementations,
>>
>
>
>> we can introduce Primality Proving algorithms.
>>
>> Some sites:
>> Basic Prime Number finding -
>> Prime Numbers - http://mathworld.wolfram.com/PrimeNumber.html (good site
>> to learn the ins/outs of prime numbers)
>> Primality Proving - http://primes.utm.edu/
>>
>> Also, we can work on implementing optimized algorithms...I think that
>> would be fun. The practical purpose of Prime Numbers can be extended
>> into encryption/decryption algorithms, but implementing those algorithms
>> might be beyond the scope of this project.
>>
>
> Actually, this (optimized algorithms for primality testing /
> generating large primes) is what would fit into the scope and mandate
> of [math] and could also be eventually useful to [OpenPGP]
> (contributing to direct pgp impl or key generation either there or in
> [math]). We have tried up to now to stick with applied math topics in
> [math], so what we should be focussed on in number-theoretic topics is
> things with applications to areas like crypto, using standard
> algorithms with good performance and accuracy.   Starting by doing
> some research on primality testing algorithms that perform well for
> large numbers would be good.  The references here provide a good
> starting point:
> http://en.wikipedia.org/wiki/Primality_test
> http://en.wikipedia.org/wiki/Miller-Rabin_primality_test
>
> I think an API for primality testing (designed consistently with the
> rest of [math] - look at the distributions, analysis, stat packages
> for examples) with implementations of some standard algorithms would
> make a great addition to [math]. The probablilistic algorithms could
> leverage the stuff in the random package and also give us some
> motivation to extend the capabilities there to include faster random
> integer generation methods.
>
> Thanks again for your interest in [math].
>
> Phil
>
> Phil
>
>
>
> Phil
>
>
>> Thanks,
>> -Sharon
>>
>> Phil Steitz wrote:
>>
>>> Hi Sharon,
>>>
>>> This sounds interesting. Can you describe a little more what
>>> algorithms you are thinking about implementing?  Online references to
>>> point us to a common set of definitions for discussion purposes would
>>> be great.
>>>
>>> Also, if you have not aldeady read this, have a look at
>>> http://jakarta.apache.org/commons/math/developers.html for info on how
>>> to get set up, etc.
>>>
>>> Thanks!
>>>
>>> Phil
>>>
>>> On 3/10/06, Sharon Lourduraj <sharon.lourduraj@gmail.com> wrote:
>>>
>>>
>>>> Hello,
>>>>
>>>> As you know every math library needs to have a relation to prime number
>>>> algorithms, so just wondering if drafting something for prime number
>>>> library would be a good idea. I am thinking of providing a patch with
>>>> very (very) basic prime number functions. What do you think?
>>>>
>>>> Let me know :-)
>>>> -Sharon
>>>>
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>>>>
>>>>
>>>>
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>>>
>>>
>>>
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>>
>>
>
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