Copeland-Erdős number

The Copeland-Erdős number , named after Arthur Herbert Copeland and Paul Erdős , is a real number from the field of number theory , which is a normal number in the decimal system , that is, all digits and blocks of digits occur in it with the same asymptotic relative frequency.

It is formed by arranging all prime numbers according to their size as decimal places. There is a zero in front of the comma.

In the decimal system, the first digits are:

C ₁₀ = 0.235711131719232931374143 ...

It is the sequence A33308 in OEIS .

The Copeland-Erdős number can also be expressed as a series:

${\displaystyle C_{10}=\sum _{n=1}^{\infty }p_{n}10^{-\left(n+\sum _{k=1}^{n}\lfloor \log _{10}{p_{k}}\rfloor \right)}}$

with as the nth prime number . ${\displaystyle p_{n}}$

Web links

• Eric W. Weisstein : Copeland-Erdos Constant . In: MathWorld (English).

Individual evidence

1. ↑ AH Copeland, P. Erdős: Note on Normal Numbers. In: Bull. Amer. Math. Soc. , 52, 1946, pp. 857-860