20200329, 22:57  #1  
Nov 2016
2088_{10} Posts 
Carol / Kynea half squares
Quote:


20200329, 22:59  #2  
Nov 2016
2^{3}·3^{2}·29 Posts 
Quote:


20200329, 23:01  #3 
Nov 2016
2^{3}·3^{2}·29 Posts 
Can someone find a prime of the form ((81^n1)^22)/2, ((215^n1)^22)/2, ((319^n1)^22)/2, ((73^n+1)^22)/2, ((109^n+1)^22)/2, ((205^n+1)^22)/2, etc?

20200329, 23:41  #4 
"Serge"
Mar 2008
Phi(3,3^1118781+1)/3
2×23×197 Posts 
It is very easy.
((205^3651+1)^22)/2 ((205^4133+1)^22)/2 ((205^4620+1)^22)/2 ((215^126941)^22)/2 ((319^112761)^22)/2 ((319^55131)^22)/2 ((73^1275+1)^22)/2 ((73^2004+1)^22)/2 etc However, the problem with these halfnearsquares is that you will not be able to prove (most of) them. (Take these PRP1 and PRP+1: there is nothing immediately smooth about them.) 
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