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Tag Archives: Mersenne
MaBloWriMo 5: The LucasLehmer 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 LucasLehmer test is a way to tell us whether is prime, for any prime . The … Continue reading
Posted in algebra, arithmetic, computation, famous numbers, iteration, modular arithmetic, number theory, primes
Tagged lehmer, lucas, MaBloWriMo, Mersenne, prime, proof, test
3 Comments
MaBloWriMo 4: not all primeindex 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
Posted in algebra, arithmetic, computation, famous numbers, iteration, modular arithmetic, number theory, primes
Tagged lehmer, lucas, MaBloWriMo, Mersenne, prime, proof, test
1 Comment
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
Posted in algebra, arithmetic, computation, famous numbers, iteration, modular arithmetic, number theory, primes
Tagged lehmer, lucas, MaBloWriMo, Mersenne, prime, proof, test
1 Comment
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
Posted in algebra, arithmetic, computation, famous numbers, iteration, modular arithmetic, number theory, primes
Tagged lehmer, lucas, MaBloWriMo, Mersenne, prime, proof, test
1 Comment
MaBloWriMo: The LucasLehmer 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
Posted in algebra, arithmetic, computation, famous numbers, iteration, modular arithmetic, number theory, primes
Tagged lehmer, lucas, MaBloWriMo, Mersenne, prime, proof, test
5 Comments
Mersenne primes and the LucasLehmer 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
Posted in arithmetic, computation, famous numbers, iteration, modular arithmetic, number theory, primes
Tagged lehmer, lucas, Mersenne, prime, test
3 Comments
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 HansMichael Elvenich in Langenfeld, Germany, is an 11,185,272digit number which you can download here. The … Continue reading
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
Posted in computation, famous numbers, links, primes
Tagged announcement, discovery, GIMPS, Mersenne, prime
1 Comment