论文标题
无条件的主要代表功能，之后
Unconditional Prime-representing Functions, Following Mills
论文作者
论文摘要
米尔斯证明存在一个真正的常数$ a> 1 $，因此对于所有$ n \ in \ mathbb {n} $，值$ \ lfloor a^{3^n} \ rfloor $都是质数。没有$ a $的明确值，但是假设Riemann假设可以选择$ a = 1.3063778838 \ ldots。 $ a = 1.00536773279814724017 \ ldots $可以计算为数百万个数字。同样，$ \ lfloor a^{3^{13n}} \ rfloor $是PRIME，$ a = 3.8249999807343914617161555551375 \ ldots。$ $。
Mills proved that there exists a real constant $A>1$ such that for all $n\in \mathbb{N}$ the values $\lfloor A^{3^n}\rfloor$ are prime numbers. No explicit value of $A$ is known, but assuming the Riemann hypothesis one can choose $A= 1.3063778838\ldots .$ Here we give a first unconditional variant: $\lfloor A^{10^{10n}}\rfloor$ is prime, where $A=1.00536773279814724017\ldots$ can be computed to millions of digits. Similarly, $\lfloor A^{3^{13n}}\rfloor$ is prime, with $A=3.8249998073439146171615551375\ldots .$
