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Old 2011-09-05, 19:13   #1
siegert81
 
Dec 2010

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Default 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?
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Old 2011-09-05, 23:00   #2
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Quote:
Originally Posted by siegert81 View Post
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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