Ranks... - Page 2

garo · 2002-08-20, 02:11

How about using math related titles?

One example:

Euclid
Archimedes
Eratosthenes
Euler
Gauss
Fermat
Sophie (Germain)
Mersenne
Reimann
etc.

Of course trying to sort the above names into order of importance would be a controversial task.

Another example:
Prime Number
Mersenne Number
Sophie Number
Fermat Number
Amicable Number
Perfect Number

in increasing order of rarity......
You could also add Mersenne Prime and then Fermat Prime of which only 39 and 4 are known respectively. You get the drift......
Garo

Tasuke · 2002-08-20, 02:15

FYI, there are equally as many of perfect numbers as there are Mersenne Primes. A perfect number is (2^p-1)((2^p) -1) if M(p) is prime

garo · 2002-08-20, 02:28

Yeah Tasuke,
That's why in the list Mersenne Numbers - of which there are infinite is higher up than Perfect Numbers. And Mersenne Prime would come at the same level as Perfect Number. Anyway this is not a mathematically sound system since theoretically there are infinite numebr of primes and therefore infinite number of Mersenne Numbers. But it's just a set of catchy math related names. The ordering will have to be a bit arbitrary....

Digital Concepts · 2002-08-20, 03:01

# of perfect numbers > # of Mersenne primes; because there are perfect numbers that are not Mersenne primes.

Kevin · 2002-08-20, 03:11

No, there are an equal number of mersenne primes and perfect numbers.
If 2^p -1 is prime, then {2^(p-1)} * {2^p -1} is a perfect number.
And that's the only way to get perfect numbers, so for every mersenne prime, there is a corresponding perfect number

Digital Concepts · 2002-08-20, 03:53

Gosh, I hadn't realized that was the only way.

Garo, many apologies!

ops:

Xyzzy · 2002-08-20, 06:20

What just happened? My head hurts!

:)

2002-08-20, 22:14

There could be more perfect numbers than mersenne primes because there may be those odd perfect numbers that are not in the form of (2^(p-1))((2^p) -1) where 2^p-1 is prime(mersenne prime).

Kevin · 2002-08-20, 23:06

"Mathematicians have so far proved that if an odd perfect number exists, it must have at least 300 digits, and at least 29 prime factors (not necessarily distinct)."
Mathematical Treks by Ivans Peterson

Since one hasn't been discovered, and they haven't been proven to exist, I assumed they didn't, and just left them out.

[edit] Probably should've mentioned that the first time. Disregarding that case was bad mathematical form. I was going for a simple answer, but I'll remember to include all the assumptions / weird cases for math stuff in the future. [/edit]

Xyzzy · 2002-08-23, 21:16

I am going to put the ranks on hold for a while... They generate a lot of database queries and they really add nothing useful to the forum... Possibly in the future we will use that space for something more interesting...

Tasuke · 2002-08-23, 21:30

Not an hour after I go up to the next rank. Man you are quick. :( ;)

2002-08-20, 02:11	#12
garo Aug 2002 Termonfeckin, IE 2²·691 Posts	How about using math related titles? One example: Euclid Archimedes Eratosthenes Euler Gauss Fermat Sophie (Germain) Mersenne Reimann etc. Of course trying to sort the above names into order of importance would be a controversial task. Another example: Prime Number Mersenne Number Sophie Number Fermat Number Amicable Number Perfect Number in increasing order of rarity...... You could also add Mersenne Prime and then Fermat Prime of which only 39 and 4 are known respectively. You get the drift...... Garo

2002-08-20, 02:15	#13
Tasuke Aug 2002 2³·3² Posts	FYI, there are equally as many of perfect numbers as there are Mersenne Primes. A perfect number is (2^p-1)((2^p) -1) if M(p) is prime

2002-08-20, 02:28	#14
garo Aug 2002 Termonfeckin, IE 2²·691 Posts	Yeah Tasuke, That's why in the list Mersenne Numbers - of which there are infinite is higher up than Perfect Numbers. And Mersenne Prime would come at the same level as Perfect Number. Anyway this is not a mathematically sound system since theoretically there are infinite numebr of primes and therefore infinite number of Mersenne Numbers. But it's just a set of catchy math related names. The ordering will have to be a bit arbitrary....

2002-08-20, 03:01	#15
Digital Concepts Aug 2002 66₈ Posts	# of perfect numbers > # of Mersenne primes; because there are perfect numbers that are not Mersenne primes.

2002-08-20, 03:11	#16
Kevin Aug 2002 Ann Arbor, MI 110110001₂ Posts	No, there are an equal number of mersenne primes and perfect numbers. If 2^p -1 is prime, then {2^(p-1)} * {2^p -1} is a perfect number. And that's the only way to get perfect numbers, so for every mersenne prime, there is a corresponding perfect number

2002-08-20, 03:53	#17
Digital Concepts Aug 2002 36₁₆ Posts	Gosh, I hadn't realized that was the only way. Garo, many apologies! ops:

2002-08-20, 06:20	#18
Xyzzy "Mike" Aug 2002 2⁵·257 Posts	What just happened? My head hurts! :)

2002-08-20, 22:14	#19
9581₁₀ Posts	There could be more perfect numbers than mersenne primes because there may be those odd perfect numbers that are not in the form of (2^(p-1))((2^p) -1) where 2^p-1 is prime(mersenne prime).

2002-08-20, 23:06	#20
Kevin Aug 2002 Ann Arbor, MI 433 Posts	"Mathematicians have so far proved that if an odd perfect number exists, it must have at least 300 digits, and at least 29 prime factors (not necessarily distinct)." Mathematical Treks by Ivans Peterson Since one hasn't been discovered, and they haven't been proven to exist, I assumed they didn't, and just left them out. [edit] Probably should've mentioned that the first time. Disregarding that case was bad mathematical form. I was going for a simple answer, but I'll remember to include all the assumptions / weird cases for math stuff in the future. [/edit]

2002-08-23, 21:16	#21
Xyzzy "Mike" Aug 2002 2⁵·257 Posts	I am going to put the ranks on hold for a while... They generate a lot of database queries and they really add nothing useful to the forum... Possibly in the future we will use that space for something more interesting...

2002-08-23, 21:30	#22
Tasuke Aug 2002 2³×3² Posts	Not an hour after I go up to the next rank. Man you are quick. :( ;)