User talk:Xario

Welcome!

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$$g_n < \sqrt{p_{n+1}}+\sqrt{p_n}.$$ Reverted.
Here is a correction I did and why.

$$g_n < \sqrt{p_{n+1}}+\sqrt{p_n}.$$ Reverted.

If $$g_n = p_{n+1} - p_n$$ denotes the nth prime gap, then Andrica's conjecture can also be rewritten as $$g_n < 2\sqrt{p_n} + 1$$.

Proof:

$$\sqrt{p_{n+1}} - \sqrt{p_n} < 1 $$

$$\sqrt{p_{n+1}} < 1 + \sqrt{p_n}$$

squared is: $$(\sqrt{p_{n+1}})^2 < (1 + \sqrt{p_n})^2 $$

$$p_{n+1} < 1^2 + 2*\sqrt{p_n} + \sqrt{p_n}^2$$

$$p_{n+1} < 1 + 2*\sqrt{p_n} + p_n$$

$$g_n = p_{n+1} - p_n $$, so

$$g_n < 2\sqrt{p_n} + 1$$

Done. If you have a better way to write it to make it clear, let me know. John W. Nicholson (talk) 23:42, 5 September 2012 (UTC)

von Hagens video
I replied on the article talkpage but here is the Daily Planet 2007 plastination video on youtube. Staircase to secret lab is at 5:17. Δρ.Κ. λόγοςπράξις 22:34, 17 August 2015 (UTC)

ArbCom elections are now open!
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