Quote:
Originally Posted by ATH
The 5 chains are only length 2.
The next steps 2^{p+2}  7 are composite and the first 4 of them are square numbers:
p=2: 2^{p+2}  7 = 3^{2}
p=3: 2^{p+2}  7 = 5^{2}
p=5: 2^{p+2}  7 = 11^{2}
p=13: 2^{p+2}  7 = 181^{2}
p=19: 2^{p+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