rnd() looks random until you understand it. So does a Mersenne Twister output, which I believe is the core of most Monte Carlo cycles.
Quote:
The distribution of prime numbers is quite random.
Is it? Or is the rationale behind the distribution not described yet. Is it an artifact of what creates it?
The rationale is well understood. The marvelous thing about it, is that it produces (or generates) sequences of numbers that closely match your criteria of what 'random sequence' is.
Quote:
At the end of the day, is it going to have a positive impact on the human condition in the short, (5-10 year), term?
They're very busy at the LHC! :) As you may be aware, the physics at this level is concerned primarily with probabilities...
holy mackerel, I transposed a couple letters (here) in your name, akosf. sorry, Akos! I think I suffer from an induced dyslexia that comes from looking for patterns in the primes... :)
I found a very big mistake in my conception.
The correction drastically increased the calculation time. :-(
So, i found only a 10.247.066 digits number. :-)
I found a very big mistake in my conception.
The correction drastically increased the calculation time. :-(
So, i found only a 10.247.066 digits number. :-)
It's still a valuable number, being a Euclid number. And I'm guessing taking only 2 hours to do it on laptop probably sets some kind of record (basing that on your remarkable ability to optimize the algorithms). Well done, Akos! Any of the several DC projects that are crunching prime-related data would likely benefit from your expertise. BTW, the largest know Euclid number is E_13494 (ref). How long do you figure it would take to calculate one greater than that, based on the time required for the result you achieved?
I found a very big mistake in my conception.
The correction drastically increased the calculation time. :-(
So, i found only a 10.247.066 digits number. :-)
It's still a valuable number, being a Euclid number. And I'm guessing taking only 2 hours to do it on laptop probably sets some kind of record (basing that on your remarkable ability to optimize the algorithms). Well done, Akos! Any of the several DC projects that are crunching prime-related data would likely benefit from your expertise. BTW, the largest know Euclid number is E_13494 (ref). How long do you figure it would take to calculate one greater than that, based on the time required for the result you achieved?
Hm... I can't remember exactly, but it was the E_146.6xx Euclid Number... I will check the index.
I'm a bit sad because of my stupidity, but i didn't give up the goal to find the biggest prime number. :)
I'm working on a prime test based on Fermat's little theorem.
I found a very big mistake in my conception.
The correction drastically increased the calculation time. :-(
So, i found only a 10.247.066 digits number. :-)
It's still a valuable number, being a Euclid number. And I'm guessing taking only 2 hours to do it on laptop probably sets some kind of record (basing that on your remarkable ability to optimize the algorithms). Well done, Akos! Any of the several DC projects that are crunching prime-related data would likely benefit from your expertise. BTW, the largest know Euclid number is E_13494 (ref). How long do you figure it would take to calculate one greater than that, based on the time required for the result you achieved?
Hm... I can't remember exactly, but it was the E_146.6xx Euclid Number... I will check the index.
I'm a bit sad because of my stupidity, but i didn't give up the goal to find the biggest prime number. :)
I'm working on a prime test based on Fermat's little theorem.
It takes a measure of genius to be able calculate such a large quantity efficiently while being certain of the accuracy. It then takes a measure of wisdom to recognize the fallibility we're all prone to, and to not give up because of it. Your efforts remind me a bit of Einstein with his Cosmological constant, and of Hawking with evaporation of a black hole. For ordinary folk like myself, failure to cultivate this wisdom is, I think, an open invitation for a nasty psychosis...
A couple years ago, I was working on a way to derive the Nth prime just from N. My result worked, and I did the best I could to explain the method, algorithm, and formula. I was still pretty sure that anyone else would think it was the gibberish of a lunatic, but I nevertheless sent it off to Dr. Math (after checking their FAQ and archives, as they request). Turns out the algorithm was basically what's known as The Sieve of Eratosthenes, and my method and formula were fine, but my conclusions... well, sparing everyone any boring accounts of my stupidity, suffice it to say I'm still refining them, grateful for the help from Dr. Math.
It sounds like you have matters well in hand, Akos. There should be a way to determine the performance of your algorithm ahead of time, though, and compare it to what's already known to be most efficient. Anyway, you probably don't need any help with the hardware aspect, but Dr. Math might be able to help with the choice of algorithm aspect, as well as provide advice on how to understand why the maths of one kind of algorithm for a primality test might be faster than others...
And congratulations in the meantime, for furthering the field with a record Euclid number, by a whole order of magnitude! Do it to it, Akos! :)
rnd() looks random until you
)
rnd() looks random until you understand it. So does a Mersenne Twister output, which I believe is the core of most Monte Carlo cycles.
Is it? Or is the rationale behind the distribution not described yet. Is it an artifact of what creates it?
At the end of the day, is it going to have a positive impact on the human condition in the short, (5-10 year), term?
Wave upon wave of demented avengers march cheerfully out of obscurity into the dream.
RE: rnd() looks random
)
The rationale is well understood. The marvelous thing about it, is that it produces (or generates) sequences of numbers that closely match your criteria of what 'random sequence' is.
They're very busy at the LHC! :) As you may be aware, the physics at this level is concerned primarily with probabilities...
holy mackerel, I transposed
)
holy mackerel, I transposed a couple letters (here) in your name, akosf. sorry, Akos! I think I suffer from an induced dyslexia that comes from looking for patterns in the primes... :)
RE: I could produce a
)
I am also interested in it~
but i can not visit your homepage~
Hello everyone!I'm Zhang Chi from China.I am 16 and I am a middle school student.And I love science. I want to be a scientist in the future!
Largest known prime by year
)
Largest known prime by year
2^32582657-1 it sure is a
)
2^32582657-1
it sure is a progess!
And I use my computer to compute number π（pai）
Hello everyone!I'm Zhang Chi from China.I am 16 and I am a middle school student.And I love science. I want to be a scientist in the future!
I found a very big mistake in
)
I found a very big mistake in my conception.
The correction drastically increased the calculation time. :-(
So, i found only a 10.247.066 digits number. :-)
RE: I found a very big
)
It's still a valuable number, being a Euclid number. And I'm guessing taking only 2 hours to do it on laptop probably sets some kind of record (basing that on your remarkable ability to optimize the algorithms). Well done, Akos! Any of the several DC projects that are crunching prime-related data would likely benefit from your expertise. BTW, the largest know Euclid number is E_13494 (ref). How long do you figure it would take to calculate one greater than that, based on the time required for the result you achieved?
RE: RE: I found a very
)
Hm... I can't remember exactly, but it was the E_146.6xx Euclid Number... I will check the index.
I'm a bit sad because of my stupidity, but i didn't give up the goal to find the biggest prime number. :)
I'm working on a prime test based on Fermat's little theorem.
RE: RE: RE: I found a
)
It takes a measure of genius to be able calculate such a large quantity efficiently while being certain of the accuracy. It then takes a measure of wisdom to recognize the fallibility we're all prone to, and to not give up because of it. Your efforts remind me a bit of Einstein with his Cosmological constant, and of Hawking with evaporation of a black hole. For ordinary folk like myself, failure to cultivate this wisdom is, I think, an open invitation for a nasty psychosis...
A couple years ago, I was working on a way to derive the Nth prime just from N. My result worked, and I did the best I could to explain the method, algorithm, and formula. I was still pretty sure that anyone else would think it was the gibberish of a lunatic, but I nevertheless sent it off to Dr. Math (after checking their FAQ and archives, as they request). Turns out the algorithm was basically what's known as The Sieve of Eratosthenes, and my method and formula were fine, but my conclusions... well, sparing everyone any boring accounts of my stupidity, suffice it to say I'm still refining them, grateful for the help from Dr. Math.
It sounds like you have matters well in hand, Akos. There should be a way to determine the performance of your algorithm ahead of time, though, and compare it to what's already known to be most efficient. Anyway, you probably don't need any help with the hardware aspect, but Dr. Math might be able to help with the choice of algorithm aspect, as well as provide advice on how to understand why the maths of one kind of algorithm for a primality test might be faster than others...
And congratulations in the meantime, for furthering the field with a record Euclid number, by a whole order of magnitude! Do it to it, Akos! :)