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Old 2022-05-20, 16:15   #27
paulunderwood
 
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Sep 2002
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Quote:
Originally Posted by retina View Post
The infinite product of 2×2×2×2×2×2×2... = 0

If we set p = 2×2×2×2×2×2×2... we can see that 2×2×2×2×2×2×2... = 2×p

Leading to p = 2×p

Subtract p from both side; 0 = p

Giving 2×2×2×2×2×2×2... = 0



Sadly the Mersenne number 2^∞-1 = -1, and therefore isn't prime.
\[2^{\aleph_0} - 1 = \aleph_1\] and I am not sure primeness is defined for these.
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