81–90 of 139 posts
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Your maths teacher didn't force you to memorize squares then.
I did memorize the sequence and still have it memorized, but I have to enumerate them. They don't have a "look" to them.
Here is a "theorem" I learned: every number up to 100 which looks prime, is prime, except 91. Does anyone recall its name?
49 looks prime to me. Another commentator says it doesn't count because it's a square number, but square numbers don't really have a particular "look" to me in the same way that 2-digit numbers ending in 5 or with digits summing to a multiple of 3 do.
Is there a reason we're obsessed with primes beyond aesthetics? Why does this set of numbers garner all the headlines as opposed to some other arbitrary integer sequence like the Recamán numbers [0] ? If tomorrow someone discovered a closed-form equation for the nth prime, how would mathematics/the world change? [0] https://en.wikipedia.org/wiki/Recamán%27s_sequence
Remember finding the common denominator in school, or reducing fractions to their lowest form. both require guess work to do the normally taught way, but both can be achieved using prime factorization in a "set" way that resolves to a solution.
I struggled in grade school to do fractions purely because of reducing and common denominators, but ended up tutoring people how to do them in college pre-algebra because thats when I learned about prime factors and what you can do with them.
If i had learned algebra before basic fractions i likely wouldn't had needed to dropout of high school and get a ged.
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This is a great "theorem", thank you! It's easy to determine divisibility by 2, 3, 5, and 11. 7² is also easy because it's a square. 7×13=91 is the only composite number under 100 that isn't caught by these rules.
A trick for remembering that 91 is composite is that it's of the form x² - y² (specifically 10² - 3²), so it's (x+y)(x-y) or 13 * 7.
Here is a "theorem" I learned: every number up to 100 which looks prime, is prime, except 91. Does anyone recall its name?
PSA: you can use the arrow keys to answer more quickly.
Today, at 56 years wise, I scored 34, so 90 > 80. Means I judge myself to be smart enough to put my shoes on the correct feet, still.
This reminds me of my favorite in-person magic trick to do. First, memorize all the two-digit primes. 25 numbers isn't that hard to memorize. Then, tell someone "Oh, I can instantly tell whether a number is prime or not. Give me a number, I'll tell you whether it's prime." If they tell you a number between 1 and 100, use your memorized list. Otherwise, it's a game of cold reading; if they just generated a random stri…
Also, most composites are divisible by 2, 3 or 5, all of which are very easy to check (for 3 just sum up the digits and if the result is divisible by 3, the original number is divisible by 3). 49, 77, and 91 are the only composites under 100 that is not divisible by one of those 3 numbers, making memorizing 25 numbers not even necessary. 49 and 77 are obviously composite to me making 91 the only number I bothered mem…