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Submitted via IRC for Bytram
What Is an "Almost Prime" Number?
When I saw a math paper with the phrase "almost prime" in the title, I thought it sounded pretty funny. It reminded me of the joke about how you can't be a little bit pregnant. On further thought, though, it seems like someone whose pregnancy is 6 weeks along and who hasn't yet noticed a missed period is meaningfully less pregnant that someone rounding the bend at 39 weeks who can balance a dinner plate on their belly. Perhaps "almost prime" could make sense too.
A number is prime if its only factors are 1 and itself. By convention, the number 1 is not considered to be prime, so the primes start 2, 3, 5, 7, 11, and so on. Hence, a prime number has one prime factor. A number with two prime factors, like 4 (where the two factors are both 2) or 6 (2×3) is definitely less prime than a prime number, but it kind of seems more prime than 8 or 30, both of which have three prime factors (2×2×2 and 2×3×5, respectively). The notion of almost primes is a way of quantifying how close a number is to being prime.
(Score: 2) by istartedi on Tuesday November 06 2018, @05:09AM
While n^42 definitely proves the set of 42-factor numbers is infinite because the set of primes is infinite, this proof feels a bit sterile since it only refers to raising primes to the 42nd power. The original poster who asked me to imagine infinite tapes was actually more appealing, except that it wasn't expressed in math notation. With the infinite tape image in your head, you can imagine any one of the infinite primes being scrolled into position to build any 42-factor number you desire.
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