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战巡
Posted 2014-10-29 04:11
回复 1# 957683999
世界级难题，谁能做出来谁得菲尔兹奖
$12p-3=k^2$，显然$k \mod 3=0$，那么令$k=3m$，有
\[4p-1=3m^2\]
可知$m \mod 4=1$，令$m=4n+1$，有
\[p=3n^2+3n+1\]
相当于证明这个有无穷多解
问题是这个方面的证明目前来说还非常没谱
参见en.wikipedia.org/wiki/Formula_for_primes#Prim … polynomial_functions
其中一行说道It is not even known whether there exists a univariate polynomial of degree at least 2 that assumes an infinite number of values that are prime; see Bunyakovsky conjecture. |
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