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Message boards : General discussion : Researchers are performing integer factorization using modified MRAM

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Message 132981 - Posted: 19 Sep 2019 | 2:12:57 UTC
...The Purdue/Tohoku probabilistic computer uses a p-bit, which "rapidly fluctuate" between 0 or 1. In a whitepaper published in Nature on Wednesday detailing their proof-of-concept, researchers were able to factor 945 and 35,161 into primes using an 8 p-bit machine.

____________  Message 133020 - Posted: 20 Sep 2019 | 12:48:12 UTC - in response to Message 132981.

I'm glad that didn't say, "researchers were able to factor primes". That would be a disaster for PrimeGrid LOL

Message 133021 - Posted: 20 Sep 2019 | 13:11:11 UTC - in response to Message 133020.

I'm glad that didn't say, "researchers were able to factor primes". That would be a disaster for PrimeGrid LOL

While the OP was interesting, this got me thinking... could you factor primes if you add more dimensions? For example, is there a complex solution? I'm not sure even what the rules would be when it comes to using complex numbers to factorise, does each of real and complex parts both have to be integer, or does the overall magnitude have to be integer?

In a quick bit of searching it is no surprise I'm not the first to go along this train of thought, but the more I dig, the deeper the hole gets...

Message 133023 - Posted: 20 Sep 2019 | 13:52:57 UTC - in response to Message 133021.

You could look at https://en.wikipedia.org/wiki/Gaussian_integer#Gaussian_primes.

A "usual" (rational) prime like 11 which leaves a remainder of 3 when divided by 4, is also a Gaussian prime. So it cannot be factored (except if one of the factors is a unit).

However, a "usual" (rational) prime like 13 which leaves a remainder of 1 when divided by 4, can be factored over the Gaussian integers, like this:

13 = (3 + 2i)*(3 − 2i)

So when you allow i (the imaginary unit, the square root of negative one), 13 can be factored.

This is because 13 can be written as the sum of two (rational) squares, 13 = 3^2 + 2^2.

/JeppeSN

Message boards : General discussion : Researchers are performing integer factorization using modified MRAM