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Old 2013-11-20, 12:16   #12
bloodIce's Avatar
Feb 2010

173 Posts
Default 10613583595427 is also a factor of 2^1968721+1

Originally Posted by storflyt32 View Post
2^1968721+1 has a factor 3 ...
Correct! It has a factor of 10613583595427 as well. What is so interesting in this number?
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Old 2013-11-20, 13:58   #13
Romulan Interpreter
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Jun 2011

22×7×349 Posts

22k+1=2 (mod 3), so 22k+1+1 will always be divisible by 3. Same as 22k-1, the last one is (2k-1)(2k+1), i.e. a product of two consecutive odd numbers, so one of them is divisible by 3.

So what?
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Old 2013-11-20, 22:55   #14
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"The unspeakable one"
Jun 2006
My evil lair

6,277 Posts

I have discovered a fantastic new way to factorise numbers using absolutely no compute power whatsoever. Just post is here and give it some name like "Unwilling Number" and within a few hours it will magically be factorised for you. I hope no one has patented this new method yet.
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