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 Feb25 comment The square root of a variable is negative? @RahulNarain The equality $1 = -1 * -1$ implies we are talking about real numbers. I don't make any kind of hasty generalization about the domain of $x$, or of $-1$ simply because none is possible. Trying to answer the question : what is the value of $x$ if $\sqrt{x} = -1$, that's the only answer possible. And quit trying to convert to reals all the time, it's not helping. Feb24 comment The square root of a variable is negative? @RahulNarain $x$ is equal to 1, but also equal to $-1 * -1$ and explicitly so. Taking the square root of something that is by defined as $-1 * -1$ means the result will be $-1$ Feb24 revised The square root of a variable is negative? Added details because I was fumbling with it. Feb24 revised The square root of a variable is negative? Bad mistake fixed Feb24 answered The square root of a variable is negative? Feb23 awarded Revival Feb23 comment Small primes attract large primes @MichaelHardy Thank you for your comments, I tried to fix it as best as I could. You should see why I was talking about $\sqrt{N}$ at the same time as the Sieve, now. Feb23 revised Small primes attract large primes Removed false information and added Fourier Transform link Feb23 awarded Teacher Feb2 awarded Editor Feb2 revised Small primes attract large primes Spelling Feb2 comment Small primes attract large primes I'd like to point you towards Factorial Primes as well since it is an other way people look for primes and test their surroundings. I believe those type of numbers fit the criterion of appropriate surroundings, but keeping the Sieve in mind, I can assume no generalization is possible. Feb2 answered Small primes attract large primes Feb2 awarded Student Feb2 awarded Scholar Feb2 accepted Produce piecewise monotonic function with 3 points and their slope with MATLAB Jan31 comment Produce piecewise monotonic function with 3 points and their slope with MATLAB I found this link by looking for Fritsch-Carlson. It appears pchip is very close to doing what I want it to do. Maybe I could wrap pchip in a function to use it. Do you think I'm better off reimplementing it? Jan31 asked Produce piecewise monotonic function with 3 points and their slope with MATLAB