On 2014-12-23 20:27, Daniel Asimov wrote:
Nice one!
I hadn't noticed before that 7*8*9*10 = 7!.
Are there any other numbers q for which there is a b > 0 such that
q*(q+1)*...*(q+b) = q!
It seems unlikely: q+1 through q+b must all be composite (else could not = (q-1)! ) But they also must contain multiples of every prime < q. If p is the largest prime < q, then there can be no primes between p and 2p (other than possibly q). Since 11 is the 2nd Ramanujan Prime, all n > 11 has >= 2 primes between n and 2n. But 11 can't be in [q+1, q+b] because it is prime. So 7 is the largest q that this holds for.
???
--Dan
On Dec 21, 2014, at 2:17 PM, Hans Havermann <gladhobo@teksavvy.com> wrote:
Don't forget to count down on New Year's Eve:
10*9*8*7/6/5*4*3-2+1
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