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Discover why certain prime numbers are so valuable they've been declared illegal — and how the same math that stumped ancient scholars now protects your online banking. This lesson covers Section 3.1 of OpenStax Contemporary Mathematics, exploring divisibility, prime and composite numbers, and their surprisingly high-stakes real-world applications. From shortcuts for testing divisibility to the 300-trillion-year encryption standard, the concepts here reveal the hidden architecture behind everyday digital life. In this video: • Divisibility rules for 2, 3, 4, 5, 6, 9, and 10 — including why adding a number's digits reveals divisibility by 3 and 9 • Prime vs. composite numbers explained with examples like 19 and 26, plus the special status of the number 1 • The square root shortcut: why you only need to test prime divisors up to the square root of a number (demonstrated with 2,117) • RSA-style encryption as a 'trapdoor function' — multiplying two large primes takes milliseconds, but reversing it would take a computer 300 trillion years • Illegal primes: how a 1,400-digit prime number was declared contraband under the Digital Millennium Copyright Act • Sophie Germain and Ramanujan — their contributions to prime number theory, including Sophie Germain primes (e.g., 23 → 47) and the taxicab number 1,729 • GCD and LCM applied to tiling a 570×450 cm room, synchronizing volunteer schedules, and cicadas evolving prime-number life cycles as evolutionary cryptography #OpenStax #PrimeNumbers #ContemporaryMathematics #Encryption #NumberTheory OpenStax Content adapted from "Contemporary Math", by OpenStax Licensed under CC BY 4.0. Content based on Web Version: Apr 23, 2026. Read the textbook online https://openstax.org/details/books/contemporary-mathematics Music first girl talking to me. by ikkun (ex. Barradeen) | https://soundcloud.com/ikkunwastaken Royalty Free Music by https://www.free-stock-music.com Creative Commons / Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) https://creativecommons.org/licenses/by-sa/3.0/deed.en_US
Answer the following questions based on the video lesson about integers, divisibility, prime and composite numbers, and their real-world applications. No outside knowledge is required — all answers come directly from the video.
Apply the concepts from the video — divisibility rules, prime testing, prime factorization, GCD, and LCM — to solve the problems below. Show all work and simplify fully.
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