论文标题
几个先验优点代表常数
A Couple of Transcendental Prime-Representing Constants
论文作者
论文摘要
众所周知，米尔斯（Mills）代理常数的算术性质尚不确定：我们不知道米尔斯的常数是理性还是不合理的数字。在其他主要代表常数的情况下，可以证明非理性性，但尚不清楚这些常数是代数还是先验数。通过使用Liouville或Roth的定理，关于理由的近似值，我们发现了几个可以证明是先验数字的主要代表常数。
It is well known that the arithmetic nature of Mills' prime-representing constant is uncertain: we do not know if Mills' constant is a rational or irrational number. In the case of other prime-representing constants, irrationality can be proved, but it is not known whether these constants are algebraic or transcendental numbers. By using Liouville or Roth's theorems about approximation by rationals, we find a couple of prime-representing constants that can be proved to be transcendental numbers.
