Random number generators discussion

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Meaning of period = 2^19937-1
Author:  Date: 2006-03-22 08:47
Dear Agner,

Why MT RNG is said to have a period of 2^19937-1?
The 32-bit integer version of this MT can only generate 2^32-1 integer numbers only. And it is also true for floating point numbers (only 2^32-1 distinct numbers)!

So where comes the 2^19937 period! Does it mean that MT can generate this many DISTINCT random numbers?

What to do with the array of 624 words? Are the words also random numbers?

If MT has only 2^32-1~=4x10^9 numbers, why it is said to be better than ran2, which can generate 10^18 numbers!

I'm so confused now, and I think new users like me will misunderstand the term "PERIOD" like I do! Caution should be given prior to any use!

Please explain!

Thanks a lot.

thread Meaning of period = 2^19937-1 - Ngo Minh Toan - 2006-03-22
last reply Meaning of period = 2^19937-1 new - Agner - 2006-03-23