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Old 2020-05-17, 21:07   #8
JeppeSN
 
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"Jeppe"
Jan 2016
Denmark

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Quote:
Originally Posted by ATH View Post
The 5 chains are only length 2.

The next steps 2p+2 - 7 are composite and the first 4 of them are square numbers:
p=2: 2p+2 - 7 = 32
p=3: 2p+2 - 7 = 52
p=5: 2p+2 - 7 = 112
p=13: 2p+2 - 7 = 1812
p=19: 2p+2 - 7 = 5*419429
Yes, I wonder if there is any explanation why the four of them are prime squares. Apparently not. I did check that 2^74207283 - 7 is not a square, ha ha.

Edit: It has been proved that 2^{p+2} - 7 is never going to be square again.

/JeppeSN

Last fiddled with by JeppeSN on 2020-05-17 at 21:36
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