Could you prove this proposition:the i-th prime gap p[i+1]-p[i]<=i
- To: mathgroup at smc.vnet.net
- Subject: [mg107156] Could you prove this proposition:the i-th prime gap p[i+1]-p[i]<=i
- From: a boy <a.dozy.boy at gmail.com>
- Date: Thu, 4 Feb 2010 06:27:07 -0500 (EST)
- References: <c724ed861002030412k2f8008a1x8ce30b426991a812@mail.gmail.com>
Hello! By my observation, I draw a conclusion: the i-th prime gap p[i+1]-p[i]<=i Could you give me a simple proof for the proposition? p[i+1]-p[i]<=i ==> p[n]<p[1]+1+2+..+ n-1=2+n(n-1)/2 Mathematica code: n = 1; While[Prime[n + 1] - Prime[n] <= n, n++] n Clear[i]; FindInstance[Prime[i + 1] - Prime[i] > i && 0 < i, {i}, Integers]
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- From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
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