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: 3, Funny) by takyon on Monday November 05 2018, @02:38PM (10 children)
Fake Primes
[SIG] 10/28/2017: Soylent Upgrade v14 [soylentnews.org]
(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.
(Score: 2) by DannyB on Monday November 05 2018, @05:55PM (1 child)
Not Fake Primes.
The opposite of primefulness is Highly composite numbers. [wikipedia.org] Or google for Superior Highly Composite Numbers. [wikipedia.org]
(that would be even better than having a full 640 K of memory)
Every performance optimization is a grate wait lifted from my shoulders.
(Score: 2) by Pino P on Monday November 05 2018, @06:10PM
Unless Gates's editor mistakenly cut off the end of "an easy way to factor large prime numbers" out of a large semiprime. In this sense, one would speak of factoring 3 and 5 out of 15.
(Score: 2) by DannyB on Monday November 05 2018, @05:58PM (1 child)
A scale of primeleyness from prime to infinitely composite maybe?
What would be infinitely composite? Infinity factorial? What could be more composite than multiplying together every possible number?
Every performance optimization is a grate wait lifted from my shoulders.
(Score: 2) by bzipitidoo on Wednesday November 07 2018, @04:22AM
> What could be more composite than multiplying together every possible number?
Powers of 2. The smallest n-almost prime number is 2^n.