Is there utility in implementing an LLT-like sequence for GIMPS? - Page 2

Batalov · 2019-01-21, 18:16

Well if it is central, then it will help you to know that this whole pdf is essentially a copy-paste from wikipedia, from Williams 98, etc.If you simply repeat a well-known proof, but only divide everything in it by 2, tell me, what is the value of it? Sure, it looks scientific and everything. There is a reason why it is only published in his own blog.

Don't get me wrong, Tony is a lot of things and a very entertaining person. I am talking about his PDF, not him.
Similarly, you seem to have trouble with expressions like 'Floating division in this context is quite silly.' Ok, uhm, I am reading this: it says 'Floating division in this context is silly', but you seem to take this statement personally, as if it was saying something about you. I am really curios to understand why?

Furthermore, GIMPS already has 82,589,933 ways of differently testing 2^82,589,933-1. Plus more: it has 82,589,933 ways of differently testing 2^82,589,933-1 with S₀=10. Does GIMPS need 82,589,933 more ways of differently (?) testing? I suspect that testing in terms of half values will produce the same bit patterns as some of the bitshifted S₀=10. But does it even matter?

Magnitudes don't matter. There are no magnitudes in the mod space -- it is a circle. There is no a<b (mod m)!
You seem to be obsessed with 'different magnitudes' and all that looking at truly tiny examples. While testing a real life candidate, all possible bit, byte and even long word combinations will happen. Billions of times. LL is like a huge candy-folding machine - it stretches the bitstring and folds it onto itself millions of time. After just one million iterations you are dealing with perfectly uniformly random bit data. And then CPU goes on for another 81+ million permutations of the essentially random bitstring. If it sounds like a random number generator - this is right, because it is! Mersenne Twister is much simpler but demonstrates the same concept well.

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2019-01-21, 18:16	#12
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 10010100000101₂ Posts	Well if it is central, then it will help you to know that this whole pdf is essentially a copy-paste from wikipedia, from Williams 98, etc.If you simply repeat a well-known proof, but only divide everything in it by 2, tell me, what is the value of it? Sure, it looks scientific and everything. There is a reason why it is only published in his own blog. Don't get me wrong, Tony is a lot of things and a very entertaining person. I am talking about his PDF, not him. Similarly, you seem to have trouble with expressions like 'Floating division in this context is quite silly.' Ok, uhm, I am reading this: it says 'Floating division in this context is silly', but you seem to take this statement personally, as if it was saying something about you. I am really curios to understand why? Furthermore, GIMPS already has 82,589,933 ways of differently testing 2^82,589,933-1. Plus more: it has 82,589,933 ways of differently testing 2^82,589,933-1 with S₀=10. Does GIMPS need 82,589,933 more ways of differently (?) testing? I suspect that testing in terms of half values will produce the same bit patterns as some of the bitshifted S₀=10. But does it even matter? Magnitudes don't matter. There are no magnitudes in the mod space -- it is a circle. There is no a<b (mod m)! You seem to be obsessed with 'different magnitudes' and all that looking at truly tiny examples. While testing a real life candidate, all possible bit, byte and even long word combinations will happen. Billions of times. LL is like a huge candy-folding machine - it stretches the bitstring and folds it onto itself millions of time. After just one million iterations you are dealing with perfectly uniformly random bit data. And then CPU goes on for another 81+ million permutations of the essentially random bitstring. If it sounds like a random number generator - this is right, because it is! Mersenne Twister is much simpler but demonstrates the same concept well.