20110905, 19:13  #1 
Dec 2010
2×37 Posts 
Generalized Fermat factors  why?
Why do mathematicians care about generalized Fermat factors and extended generalized Fermat factors?
I'm curious, because I've discovered three extended generalized Fermat factors myself as a result of finding some low kvalue Proth primes. 63*2^1356980 + 1 divides xGF(1356973,11,4) 229*2^484018 + 1 divides xGF(484017,11,9) 1137*2^79616 + 1 divides xGF(79615,12,7) I can understand the search for classical Fermat factors, mainly because that search is limited, but it seems arbitrary to stop the search for extended GF factors at a=12. Why not a=68, b=65? Do such discoveries aid mathematicians in any way? 
20110905, 23:00  #2  
"Mark"
Apr 2003
Between here and the
2×11×269 Posts 
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