Hey, all, I took a blog break yesterday — it’s been a long semester so far and I just decided to cut off one thing for a bit. It was…different (that’s Minnesota slang, I’ll let others translate). I’ll ease back in today.
First on the agenda: my birthday was on Friday, and I got inundated with greetings on Twitter and Facebook and all those social media places, and I did not reply to them. Not because I’m a bitter, hateful old man now, but simply because there were so dang many of them that if I tried I would have been sitting there all day typing the same short phrases over and over again. So I will now simply broadcast one mass “THANK YOU VERY MUCH. I HAD A LOVELY TIME. I’D HAVE INVITED YOU TO THE PARTY BUT THE WEATHER WAS TERRIBLE AND I DIDN’T HAVE ENOUGH CAKE. SINCERELY, PZ.” Although actually I had tacos, but if I’d told you that you would have been even more annoyed that I didn’t invite you. Sorry. But really, thanks!
For those of you hoping for news from the future, I have to tell you that so far being 61 is awesome. It’s a prime number, you know, and you get all kinds of superpowers on prime birthdays; now I have to wait 6 more years before I get another base power boost. It’s also the sum of two squares, so you get to feel as good as you did when you were 5, 6, 25, and 36, which is nice.
All in all, I highly recommend living until you are at least 61. I encourage all of you young’uns to do so.
“I’m a bitter, hateful old man now…”
Now?
Uh, PZ, I think you arithmetic is a little bit off. 61 cannot simultaneously be prime and the sum of two squares. 67 is not the sum of two squares either, so I don’t know what you are referring to. 5 is prime but 6 is neither prime nor the sum of two squares. 25 and 36 are squares, but not the sums of squares. So what is that series about? What are you trying to say?
I used to be a bitter, hateful young man.
You are still young, bitter, hateful or otherwise.
But, hay, at least you’re not dead and that’s a good thing so keep it up.
Thank you for your blog. Thank you for your knowledge. Thank you for your opinions. Thank you for being here.
Though, yes, I am a bit annoyed about the tacos.
@2 25=5*5, 36=6*6, 25+36=61 So 61 is both a prime and a sum of squares. You know, like both a floor wax *and* a dessert topping.
61 is prime.
25+36=61.
25 is the square of 5.
36 is the square of 6.
A prime cannot be the product of two squares, which might be the source of your confusion.
Ah. I see.
“A prime cannot be the product of two squares, which might be the source of your confusion.”
Math is tricky.
A google search on “list of primes” shows 61 as prime, and 73 as well, the age I just left. “73” is also what ham radio operators use to say “best wishes”. Now I am 74 – my daddy died at 74, and I had my open heart operation at 73. The op was, to all appearances, a great big success so I am set to outlive my dad, but will I make it to 83, my mother’s death age? 79 and 83 are also primes so I’m hoping for at least two more prime ages.
61 mod 12 = 1
It’s just like having your first birthday all over again. But the tacos probably didn’t need to be mashed up into some weird looking slop this time.
Ah, I wasn’t thinking of two different squares. Anyway the reference to 5, 6, 25 and 36 was not obvious as you simply said that the sum of two squares is cool. Got it now.
PZ, next year is even better – 62 (my age) is the smallest number that is the sum of 3 different squares in two different ways:
62 = 1² + 5² + 6²
62 = 2² + 3² + 7²
Not only that, 62 is the sum of 3 cubes:
62 = 2³ + 3³ + 3³ (although two are the same)
I’m looking forward to my 64th birthday – my last binary birthday (2 to the power of 6). Probably. Unless I’m really, really lucky. So far, so good.
I’m 64, which is a perfect square, but the best part is putting in for my retirement from teaching this June. I plan to work on my house, build model airplanes, watch old movies (scanning DVDs into my computer now and then, very convenient on the home network), travel and scratch anything that cries out to be scratched.
A belated happy birthday young fellow.
In an odd reverse you’ve given me a gift. I’ve finally discovered the definition of Goldbach’s conjecture while checking the list of primes. Also found that one is not a prime.
I’ve great appreciation for your writing, and speech, and rarely have even minor disagreement. (Don’t end clauses with prepositions.)
jack16
PZ, you’re not old. You’re obviously in the prime of your life! Keep on going, we need light in these dark times.
A belated birthday greeting! Oh, there’s still lots to anticipate. I got all kinds of paraphernalia when I turned (Route) 66 — a cap useful for gardening, a couple of T-shirts and an excellent map. Three years later … but there, dear reader, we shall avert our eyes.
On my next birthday my age will be the sum of an infinite number of squares (and cubes, for that matter). And while it won’t be a prime, it will be the product of two primes.
Why not?
It gives me an irrational pleasure to know that I share my birthday with you every single year. Thank you for the blog, PZ, it sheds more light than candles and contains more good stuff even than birthday cake.
Happy Birthday, PZ!
1957 was a very good year. I will join you in being 61 this September.
@15 mykroft
And just think of the sum of the knowledge he’s squared away!
Happy birthday PZ. May you work as long as you want, and have a pleasant retirement when you decide to do so.
They don’t like it. It gives them gas.
The clauses or the prepositions?
I recall hearing that if a number is (a) prime, and (b) is of the form 4x + 1, where x is an integer, it’s always the sum of two squares. E.g., 5 is prime and the sum of 4 and 1, 7 is prime but not of the form 4x + 1, 13 is prime and the sum of 9 and 4, and so on.
Happy belated birthday!
Happy Birthday!