Finally, lots of RAM for a good reason
I realized I need to study the structure of Z^*_{2^32} in detail. In particular, Carmichael's function shows there are at least 2 multiplicative subgroups within Z^*_{2^32}. I have to partition Z^*_{2^32} into all such subgroups and study them further.
At last, a reasonable way to put more than 4 gb of RAM to good use...

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