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 2003-12-29, 11:18 #1 Cyclamen Persicum     Mar 2003 34 Posts Generalized Mersenne Primes I need an information about nongenuine (generalized?) Mersenne numbers in terms of 2^a +/- 2^b +/- 2^c ... +/- 2^0, for instance, 2^384-2^128-2^96+2^32-1 is prime. I believe, they have all the advantages of regular mersenne numbers: 1) there is a fast deterministic Lucas-Lahmer-like test; 2) there is a way of simple modular reduction based on magic figure "nine" properties (I don't mean IBWDFFT here...) How can I perform the items 1 and 2 really? For example, how can I get a residue from division by 9909 in the decimal numeration? Sorry, I have forgotten completely, why are nongenuine mersenne numbers much better than regular mersenne numbers? Because there are a lot of them, contrary to 40-ty known regular ones.
 2004-01-30, 15:11 #2 Cyclamen Persicum     Mar 2003 1218 Posts Crandall Numbers Besides holed generalized mersenne numbers such as 1111111111000001111111110000000000000000000000011111111111111... there are so called CRANDALL numbers 2^n-c, where c is small. Modular reduction is easy and worth nothing for these sweet honey numbers!!! But one thing has not been seen: is there deterministic LL-test for crandall primes or one must use common rabin-miller test?

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