Bertrand's Postulate for Carmichael Numbers · HackerPapers discussions

Bertrand's Postulate for Carmichael Numbers — mentioned by sohkamyung

Fri, 14 Oct 2022 02:12:58 GMT

Interesting. Entering [ https://ar5iv.org/abs/2111.06963 ] also gives me the HTML render of the paper. Saves one step, since I don't have to fetch the PDF first. :-)

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Bertrand's Postulate for Carmichael Numbers — mentioned by renewiltord

Thu, 13 Oct 2022 20:14:44 GMT

Good tip. I should have just linked the arxiv.org page for the article and not the PDF directly https://arxiv.org/abs/2111.06963

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Bertrand's Postulate for Carmichael Numbers — mentioned by renewiltord

Thu, 13 Oct 2022 18:22:14 GMT

Summary: 1. Fermat's Little Theorem: if p is prime, then b^p = b (mod p) for all integers b. i.e. b^p - b is always a multiple of p. 8^3-8 = 512-8 = 504 = 168 x 3. 2. Is the inverse true? Does b^n - b = 0 (mod n) mean that n is prime? No. Sometimes n is non-prime (like n=561, divisible by 3). We call these n, Carmichael numbers. 3. Okay, so these numbers exist. How common are they? For primes we know they're common. Bertrand postulated (Chebyshev proved) that for any n>1, there is a prime p between n and 2n. That's cool! 4. Is it true that there is such a bound for these pretend-primes? Well…

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