Mills’ constant

Find the smallest real positive number $M$ such that $\\lfloor M^{3^{n}}\\rfloor$ is a prime number for any integer $n>0$ . This is Mills’ constant. Assuming that the Riemann hypothesis is true, the constant’s value would be approximately 1.3063778838630806904686144926026 (see A051021 in Sloane’s OEIS). According to Caldwell and Cheng, Mills’ original paper “contained no numerics,” it only proved the existence of such a number; moreover it referred to $\\lfloor M^{c^{n}}\\rfloor$ , and it is those who hunt for the specific value of $M$ who often choose $c=3$ . Armed with these assignments and assumptions (including certain probable primes), Caldwell and Cheng computed almost seven thousand base 10 digits of Mills’ constant. The first few primes generated by Mills’ constant would be 2, 11, 1361, 2521008887, etc. (listed in A051254).

References

1 C. K. Caldwell & Y. Cheng, “Determining Mills’ Constant and a Note onHonaker’s Problem” J. Integer Sequences 8 (2005): 05.4.1
2 W. H. Mills, “A prime-representing function”, Bull. Amer. Math. Soc. 53 (1947): 604

单词	MillsConstant
释义	Mills’ constant Find the smallest real positive number $M$ such that $\\lfloor M^{3^{n}}\\rfloor$ is a prime number for any integer $n>0$ . This is Mills’ constant. Assuming that the Riemann hypothesis is true, the constant’s value would be approximately 1.3063778838630806904686144926026 (see A051021 in Sloane’s OEIS). According to Caldwell and Cheng, Mills’ original paper “contained no numerics,” it only proved the existence of such a number; moreover it referred to $\\lfloor M^{c^{n}}\\rfloor$ , and it is those who hunt for the specific value of $M$ who often choose $c=3$ . Armed with these assignments and assumptions (including certain probable primes), Caldwell and Cheng computed almost seven thousand base 10 digits of Mills’ constant. The first few primes generated by Mills’ constant would be 2, 11, 1361, 2521008887, etc. (listed in A051254). References 1 C. K. Caldwell & Y. Cheng, “Determining Mills’ Constant and a Note onHonaker’s Problem” J. Integer Sequences 8 (2005): 05.4.1 2 W. H. Mills, “A prime-representing function”, Bull. Amer. Math. Soc. 53 (1947): 604
随便看	abelian variety AbelPrize Abel Prize AbelsLemma AbelsLimitTheorem AbelsMultiplicationRuleForSeries AbelSummability Abel summability Abel’s lemma Abel’s limit theorem Abel’s multiplication rule for series ABIsConjugateToBA AB is conjugate to BA AbnormalSubgroup abnormal subgroup AbsoluteConvergenceImpliesConvergenceForAnInfiniteProduct absolute convergence implies convergence for an infinite product AbsoluteConvergenceImpliesUniformConvergence absolute convergence implies uniform convergence AbsoluteConvergenceOfDoubleSeries absolute convergence of double series AbsoluteConvergenceOfInfiniteProduct absolute convergence of infinite product AbsoluteConvergenceOfInfiniteProductAndSeries absolute convergence of infinite product and series