[seqfan] Re: More (composite) terms for A233281
Hans Havermann
gladhobo at teksavvy.com
Thu Feb 13 21:11:18 CET 2014
"The smallest prime factor of Fib(p) being ~ 2p suggests that the smallest composite divisor of Fib(p) exceeds ~ 4*p^2."
Correction: The smallest possible prime factor of Fib(p) is 2*p-1, the second-smallest possible prime factor is 4*p+1; therefore the smallest possible composite divisor of Fib(p) is 8*p^2-2*p-1. For example, (p=37) 73*149, (p=97) 193*389, etc. This makes it possible to get all of Antti's composites < 10^11 by looking at Fibonacci factorizations up to (and including) Fib(111799). Doing so yields 338 (barring errors) composites. I've got the second non-semiprime (1453*2909*10177) as #254.
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