Fun Stuff > CHATTER
Can't Think of a Breaking Bad Pun For the Title: Let's Do Some Math!
Loki:
I got the third before clicking on the solution! (And I had already heard the second before)
Carl-E:
Max Zorn - yes, the Zorn of Zorn's lemma - was a professor emeritus at Indiana when I was in grad school. In his 80's, he would come to every colloquium and seminar, and always had an insightful comment or question or two. He lunched at Mother Bear's pizza with his wife over a pitcher of beer, then spent the afternoons in the seminars. I taped up a couple of white index cards behind the coffee pots for him so he could see when the coffee was still brewing and not pull the pot out too early.
The story around the department was that at a party sometime in the late 50's, he got very drunk, got up on a table, and loudly pronounced "It's not a lemma, and it's not mine!"
Loki:
Woha. I am completely :psyduck: right now
Carl-E:
It's my birthday today. My age is the next to last prime sum of two squares before the usual retirement age (65 in the US).
:-D
Loki:
Happy birthday!
How'd one go about solving this analytically?
(click to show/hide)Okay, you said prime. That means is is odd - and it's the sum of two numbers, it means that one of the numbers is odd and the other is even. The biggest square of an even number which is lower than 65 is 49 - leaving plenty of space to find the second square.
65 - 49 = 16 => consider all square of even numbers whose square is lower than 16.
Also, the result must be prime.
The only left would be 53. Okay, that probably won't work, as you said second-to-last. Let's check the next one.
7^2+1^2 is not prime.
Consider 6^2 = 36. Then the other number must be odd.
65 - 36 = 29. The next-smallest square of an odd number is 25. 25 + 36 = 61, which is also conveniently the largest prime smaller than 65.
At this point, I thought about writing "Happy 53rd birthday?"
Wait, what about 59.
...It is at this point I half-remembered some half-forgotten piece of trivia that there is something about prime numbers and sums of two squares. Googling brought up http://en.m.wikipedia.org/wiki/Fermat%27s_theorem_on_sums_of_two_squares which conveniently lists some of the numbers for which this property holds. AND ALSO WOULD HAVE CONSIDERABLY SPED UP THE PROCESS HAD I FOUND IT SOONER!
Particularly, it does not hold for 59.
Happy 53rd birthday?
You devious bastard. You nerdsniped me for at least 15 minutes. Congratulations :D
Navigation
[0] Message Index
[#] Next page
[*] Previous page
Go to full version