mersenneforum.org Generalized Fermat factors - why?
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 2011-09-05, 19:13 #1 siegert81   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 k-value 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?
2011-09-05, 23:00   #2
rogue

"Mark"
Apr 2003
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Quote:
 Originally Posted by siegert81 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 k-value 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?
Since Wilfrid Keller collects them, you should ask him.

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