2^(2^31-1) - 1 is composite. It has known 'small' factors 295257526626031 (found in 1983 by Guy Haworth), 87054709261955177 (1994, Wilfrid Keller), and 242557615644693265201 = 112949691600*(2^31-1) + 1 (December 1999, Reto Keiser).
T.
Dear Prime community, � please be aware of the following: � 2^2-1 = 3 (Mersenne prime) � 2^3-1 = 7 (Mersenne prime) � 2^7-1 = 127 (Mersenne prime) � 2^127-1 = ca. 2.3E+18�(Mersenne prime) � 2^ca. 2.3E+18 -1 = probably a further Mersenne prime � My hypothesis: Starting with one-digit primes, you can use a Mersenne prime as Mersenne exponent to yield a further Mersenne prime. � Because today we cannot proove the primarity of 2^ca. 2.3E+18 -1 let me suggest to investigate 2^31-1 as a Mersenne exponent: � 2^5-1 = 31 (Mersenne prime) � 2^31-1 = 2 147 483 647 (Mersenne prime) � 2^2147483647-1 = Next Mersenne prime ? � Using a single PC it would take me about 600 years to check this. Using the GIMPS project it should be feasible. � What do you think about that? � Best regards, Dr. Roland Linder � � _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
-- Tony _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
