carol prime numbers?

Question

can anyone give me some information on carol g. kirnon ( the origonator of the carol prime number), it's for my sons homework assignment

Answer 1

You may find this dialogue excerpted from a prime number discussion group informative. It suggests that the "inventor" of the Carol prime, named them after a high-school girlfriend.

Aloha


Re: Farewell to Kynea, Carol, Noddy and Big-Ears

Dear Cletus,

The two years that I had in mind were between your posting:

http://groups.yahoo.com/group/primenumbers/message/5116

> Wed Feb 6, 2002 12:02 am

> Also, there is another set of numbers called Kynea Numbers.
> They are of the form K[p]= 4^p + 2^(p+1) - 1.
> They have exactly the same properties as Carol Numbers.

and this one:

http://groups.yahoo.com/group/primenumbers/message/14584

> Mon Feb 23, 2004 5:11 pm

> Carol G. Kirnon is my best female friend in the whole wide world.
> She was the first girl to steal my heart when we were in high
> school. Therefore, since math is my love and she is my love, I
> named the first set of numbers after her. The second set, and
> really the second set, because I encountered them days after is
> named for the baby girl that had the greatest inpact on my life
> so far, Kynea R. Griffith (she is ten years old now).

If you can point to some place between these dates
where you explained your choices of name,
then I shall humbly apologize.

I fully understand that these names are very dear to you.

However, I object to your apparent lack of candour in the 2 years
when these names were accumulating web hits in amateur
mathematical circles, for no good reason except that you seem to
regard giving unexplained names to unpublished mathematical
formulas to be your personal prerogative.

David

Answer 2

Carol number
From Wikipedia, the free encyclopedia
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A Carol number, named after Carol G. Kirnon, is an integer of the form 4n − 2n + 1 − 1. An equivalent formula is (2n − 1)2 − 2. The first few Carol numbers are: −1, 7, 47, 223, 959, 3967, 16127, 65023, 261119, 1046527 (sequence A093112 in OEIS).

For n > 2, the binary representation of the nth Carol number is n − 2 consecutive ones, a single zero in the middle, and n + 1 more consecutive ones, or to put it algebraically,

\sum_{i \ne n + 2}^{2n} 2^{i - 1}

So, for example, 47 is 101111 in binary, 223 is 11011111, etc. The difference between the nth Mersenne number and the nth Carol number is 2n + 1. This gives yet another equivalent expression for Carol numbers, (22n − 1) − 2n + 1. The difference between the nth Kynea number and the nth Carol number is the (n + 2)th power of two.

Starting with 7, every third Carol number is a multiple of 7. Thus, for a Carol number to also be a prime number, its index n cannot be of the form 3x + 2 for x > 0. The first few Carol numbers that are also prime are 7, 47, 223, 3967, 16127 (these are listed in Sloane's A091516). As of 2005, the largest known Carol number that is also a prime is the Carol number for n = 226749, approximately 3.16937497264887779 × 10136516. It was found by Steven Harvey in early 2005, using MultiSieve and PrimeForm. It is the 38th Carol prime. These numbers were first encountered by Cletus Emmanuel in 1994, who consequently named them

Answer 3

I can't type maths properly in this, but a carol number is a number of a particular form, some of which are prime under certain conditions for its index.

Google it and check the wiki below for more

Answer 4

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Answer 5

nicely, she'll turn heads 50% of the time, so she's have been given a a million in 2 probability of flipping heads. and a die has the numbers a million-6 on it. a million,2, and 5 are best, so as that ought to indicate she has a three in 6, or 1in 2 probability of rolling a primary huge type. So, to make certain the risk of flipping heads and rolling a primary huge type on the identical time, you will multiply the two percentages jointly: a million/2 x a million/2=a million/4. which ability a million/4 of the time, she'll get heads and a primary huge type. seeing that she did it forty circumstances, which ability she'll get heads and a primary 10 circumstances.

Answer 6

Please disregard Carol G. Kirnon. We're going to find out the discoverer(s) of Carol numbers and Carol primes later.

Answer 7

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Answer 8

http://www.answers.com/topic/carol-number

Answer 9

http://en.wikipedia.org/wiki/Carol_number


Doug