# Tag Archives: Mersenne

## MaBloWriMo 5: The Lucas-Lehmer Test

We now know that can only be prime when is prime; but even when is prime, sometimes is prime and sometimes it isn’t. The Lucas-Lehmer test is a way to tell us whether is prime, for any prime . The … Continue reading

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## MaBloWriMo 4: not all prime-index Mersenne numbers are prime

Over the past couple days we saw that if is composite, then is also composite. Equivalently, this means that if we want to be prime, then at the very least must also be prime. But at this point there is … Continue reading

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## MaBloWriMo 3: Mersenne composites in binary

Yesterday we saw that must be composite, since . Today I’ll talk about a somewhat more intuitive way to see this. Recall that we can write numbers in base 2, or “binary”, using the digits 0 and 1 (called “bits”, … Continue reading

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## MaBloWriMo: Mersenne composites

The name of the game is to find Mersenne numbers which are also prime. Today, a simple observation: can only be prime when is also prime. Put conversely, if is composite then is also composite. For example, is composite and … Continue reading

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## MaBloWriMo: The Lucas-Lehmer test

Today, I noticed both Zachary Abel and Qiaochu Yuan plan to write a blog post every day this month (hooray!). I haven’t written on here as much as I would like recently, and so I thought, why not? I already … Continue reading

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## Mersenne primes and the Lucas-Lehmer test

Mersenne numbers, named after Marin Mersenne, are numbers of the form . The first few Mersenne numbers are therefore , , , , , and so on. Mersenne numbers come up all the time in computer science (for example, is … Continue reading

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## Two Very Large primes

As promised, I can now reveal the identity of the two newly discovered Mersenne primes. The smaller of the two, discovered on September 6 by Hans-Michael Elvenich in Langenfeld, Germany, is an 11,185,272-digit number which you can download here. The … Continue reading

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## New Mersenne primes!

The Great Internet Mersenne Prime Search just announced not one, but two new Mersenne primes! You might also recall the last time they announced a new prime, in September 2006, so these new primes were found almost exactly two years … Continue reading

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