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Not sure if this is really an adequate question here, but I found no other place to turn. I'll understand if this gets closed.

I recently learned about the GIMPS project, and installed it on my computer. However, I'm confused as to what it's actually doing. Mainly, I want to be able to know which numbers it's actually testing, and possibly some information about the algorithms it employs.

For example, a window might have as a header:

Worker #2 - 88.66% of M38006351

How do I know what number this M$\cdots$ is? An online test showed in very little (imperceptible) time that $38006351$ is indeed prime, but then, why is it taking hours, or days to reach a conclusion? Naturally, the online tester I used could be taking it from a known list, but then why am I testing for it? Or does it take known primes, and test if they are Mersenne? (I'm not exactly versed in number theory so that may be an absurd proposal). Clearly something is wrong, or the M$\cdots$ stands for a different number altogether.

I've also tried searching the webstie, which reveled nothing, and pressing F1 for help, which gave an error message. Again I apologize if this is out of place.

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It is checking the number $2^{38006351}-1$ which has more than ten million digits.

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  • $\begingroup$ Great, thanks! Is the M- just standard notation? $\endgroup$ – GPerez Jan 10 '15 at 1:33
  • $\begingroup$ @GPerez: A more standard notation would be $M_{38006351}$, but window titles (and other raw strings in programs not specifically made to display mathematics nicely) can't easily contain the subscript, so it all gets jammed together to M38006351. $\endgroup$ – Henning Makholm Jan 10 '15 at 1:46

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