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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 requerdanos on Monday November 05 2018, @04:50PM (5 children)
Consider that you can substitute the word "not" for the word "almost" anywhere it's grammatically allowable and have a less ambiguous, easier-to-evaluate version that retains the truth of the original statement.
One of the truisms that I am proud to have taught my son is that if you're in doubt about the meaning of a statement containing the word "almost", remember that almost means "not".
(Score: 1, Informative) by Anonymous Coward on Monday November 05 2018, @05:06PM (2 children)
Playing the lottery almost always leads to a loss.
Playing the lottery not always leads to a loss.
Sure, both statements are true. But the first one contains more useful information.
(Score: 2) by requerdanos on Monday November 05 2018, @05:22PM
You probably weren't in doubt, as the author of at least the headline of this story seems to be.
(Score: 2) by kazzie on Monday November 05 2018, @06:26PM
The second statement is better for marketing purposes, though.
(Score: 2) by Pino P on Monday November 05 2018, @05:56PM (1 child)
Is "some composite numbers are more composite than others, and this difference may be useful for some purpose in number theory" more honest?
(Score: 2) by requerdanos on Monday November 05 2018, @06:40PM
In this case, the following statements can be true (let x=26, for example):
"x is not prime"
"x is less composite than other not-prime numbers of similar magnitude in terms of number of factors"
So no, something completely true about a number's being prime or not is not more honest than something completely true about a number's set of available factors. Each statement tells you something completely true about the number.
If you're in doubt, remember that "almost prime" means that a number isn't prime, and so you're talking about its properties as a composite number. If you're not in doubt, then this probably won't help you.