Happy Birthday RKNRUSTY

Now only one year away from being a sexagenarian but, nevertheless, 59 is an interesting number.

Fifty-nine is the 17th smallest prime number. The next is sixty-one, with which it comprises a twin prime. 59 is an irregular prime, a safe prime and the 14th supersingular prime. It is an Eisenstein prime with no imaginary part and real part of the form 3n - 1. Since 15! + 1 is divisible by 59 but 59 is not one more than a multiple of 15, 59 is a Pillai prime.

It is also a highly cototient number.

In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above one and has more solutions to the equation x − φ(x) = k, than any other integer below k and above one. Here, φ is Euler's totient function. There are infinitely many solutions to the equation for k = 1 so this value is excluded in the definition. The first few highly cototient numbers are:[1]
2, 4, 8, 23, 35, 47, 59, 63, 83, 89, 113, 119, 167, 209, 269, 299, 329, 389, 419, 509, 629, 659, 779, 839, 1049, 1169, 1259, 1469, 1649, 1679, 1889, ... (sequence A100827 in OEIS)
There are many odd highly cototient numbers. In fact, after 8, all the numbers listed above are odd, and after 167 all the numbers listed above are congruent to 29 modulo 30.

The concept is somewhat analogous to that of highly composite numbers. Just as there are infinitely many highly composite numbers, there are also infinitely many highly cototient numbers. Computations become harder, since integer factorization does, as the numbers get larger.

The first few highly cototient numbers which are primes are 2, 23, 47, 59, 83, 89, 113, 167, 269, 389, 419, 509, 659, 839

There are 59 stellations of the icosahedron.

59 is one of the factors that divides the smallest composite Euclid number. In this case 59 divides the Euclid number 13# + 1 = 2 * 3 * 5 * 7 * 11 * 13 + 1 = 59 * 509.

59 is the atomic number of praseodymium, a lanthanide

Happy Birthday and many happy returns.

The most important thought is we hope YOU are feeling "Prime" :-)

Happy Birthday, Rusty!

George

Happy Birthday Rusty! I hope you have a great day!

HAPPY BIRTHDAY RUSTY !!!!! Hope you have a Great Day!!! Eric

Ah to be 59 again, what a youngster I just applied for Social Security.
HAPPY BIRTHDAY young man!!

HAPPY BIRTHDAY RUSTY! 

Hope you have a wonderful day and many many more to follow!

Well I can't beat Mark's gift to you, so Happy Birthday my friend!!!!!!!!!!!!!

Hey Pal,

Have an excellent day. Hope you get to spend the day doing something you really enjoy and too bad that Fox .59 wasn't for real!

Ron

Ah, now we're talkin', love the babes. That's the number one reason I'm glad I haven't gone blind yet!... even if she probably wouldn't even cut an eye in my direction anymore Lol. Good thing I married one. And yes, I am feeling prime, I feel really good. And thanks to Ian, now I know what I'm feeling. Thanks everyone! March is the best time ever for a birthday. It marks the beginning of the end of winter.

Really, I thought that engine was a bit weird to be real. Thanks everybody.
Rockin'Rusty

Happy Birthday, Rusty!

Happy Birthday Rusty!!!

HAPPY BIRTHDAY

Yak with crumpet



Sorry Rusty, this was the wrong picture. Let's say it was Google's fault. I'll try again:

Happy Birthday Sir! The pinups are a nice touch

OVERLORD wrote: HAPPY BIRTHDAY

Yak with crumpet

Sorry Rusty, this was the wrong picture. Let's say it was Google's fault. I'll try again:

On your six...

Happy birthday brother!
Glad you're feelin' good, you should,
we all wished it so.
Wait till you hit 60, it's really cool.

Bob

Hi Rusty,

remember that in a duo-decimal system you are only 51 (myself only 49 on the same platform) and whenever my long undseen friends tell me I look younger every time we meet I tell them that yes, if I continue that way, I will soon need pampers in a few yeasrs again...

Cheers from Hungary.

Happy Birthday, Brother. Hope you have Tons O' Fun!

The "Not As Old As You" Mark

OVERLORD wrote: HAPPY BIRTHDAY

Yak with crumpet

Haha, Lieven, that's funny. I had no idea a Yak would let anybody sit on it... I guess if I was a Yak, I'd let her sit on me.

Thanks everybody, I did have a great day, went out for a fried flounder dinner with Holley, and now I'm trying to decide how to spend the rest of the day. It's just past 8pm. I could go work on the Oriental. It should be ready to fly by tomorrow afternoon. Or I could watch TV, or catch another installment of Doctor Who on Netflix. Decisions decisions. Y'all take care of yourselves.
Rockin'Rusty

Oh yeah, and thanks for getting your wives and girlfriends to pose for me.
Rusty