20210701, 22:56  #23  
"James Heinrich"
May 2004
exNorthern Ontario
3504_{10} Posts 
Quote:
I first ran it through GIMPS range (<1000M): Quote:
Quote:


20210702, 14:02  #24 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2720_{16} Posts 
For a factor to be square of another factor it would still have to be a factor in its own right.
So for q to be a factor it would have to both be (2kp+1)(2kp+1) and 2Жp+1 (2kp+1)(2kp+1) = 2Жp+1 4k^{2}p^{2} + 4kp + 1 = 2Жp + 1 4k^{2}p^{2} + 4kp = 2Жp 2k^{2}p + 2k = Ж 2k(kp +1) = Ж As there any to prove that this can't be? 
20210702, 14:38  #25  
Jan 2021
California
2×3×37 Posts 
Quote:
That's why it's still open as to whether a Mersenne number can have a square (>1) as a factor. 

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