From a2dcf2aaebccf52107a6472ae8c92392c4782ede Mon Sep 17 00:00:00 2001 From: filifa Date: Sat, 19 Jul 2025 00:59:54 -0400 Subject: [PATCH] change link to avoid stray parenthesis --- notebooks/problem0007.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/notebooks/problem0007.ipynb b/notebooks/problem0007.ipynb index c86315d..0ea2501 100644 --- a/notebooks/problem0007.ipynb +++ b/notebooks/problem0007.ipynb @@ -48,7 +48,7 @@ "\n", "Consider the fact that $3^{6} \\equiv 3 \\pmod{6}$, but 6 is composite. In cases like this, we say that $p$ is a *base $a$ Fermat pseudoprime*, e.g. 6 is a base 3 Fermat pseudoprime. 6 is also a base 4 Fermat pseudoprime, but 2 and 5 both serve as witnesses to 6 being composite (we need only consider bases modulo $p$).\n", "\n", - "This may lead us to believe that we can just check every base $a$, and if there are no witnesses, then $p$ is prime. However, (along with this method being inefficient for large $p$), there are numbers that are Fermat pseudoprimes for *every* base, called [Carmichael numbers](https://en.wikipedia.org/wiki/Carmichael_number). Therefore, the [converse](https://en.wikipedia.org/wiki/Converse_(logic)) of Fermat's little theorem does not hold.\n", + "This may lead us to believe that we can just check every base $a$, and if there are no witnesses, then $p$ is prime. However, (along with this method being inefficient for large $p$), there are numbers that are Fermat pseudoprimes for *every* base, called [Carmichael numbers](https://en.wikipedia.org/wiki/Carmichael_number). Therefore, the [converse](https://w.wiki/BAyj) of Fermat's little theorem does not hold.\n", "\n", "Nevertheless, Carmichael numbers are relatively rare, so if you pick a random number to test and a few random bases, and find no witnesses, you can be pretty sure the number is in fact prime.\n", "\n",