Smarandache–Wellin number
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In mathematics, a Smarandache–Wellin number is an integer that in a given base is the concatenation of the first n prime numbers written in that base. Smarandache–Wellin numbers are named after Florentin Smarandache and Paul R. Wellin.
The first decimal Smarandache–Wellin numbers are:
A Smarandache–Wellin number that is also prime is called a Smarandache–Wellin prime. The first three are 2, 23 and 2357 (sequence A069151 in the OEIS). The fourth is 355 digits long: it is the result of concatenating the first 128 prime numbers, through 719.[1]
The primes at the end of the concatenation in the Smarandache–Wellin primes are
The indices of the Smarandache–Wellin primes in the sequence of Smarandache–Wellin numbers are:
The 1429th Smarandache–Wellin number is a probable prime with 5719 digits ending in 11927, discovered by Eric W. Weisstein in 1998.[2] If it is proven prime, it will be the eighth Smarandache–Wellin prime. In March 2009, Weisstein's search showed the index of the next Smarandache–Wellin prime (if one exists) is at least 22077.[3]
- Copeland–Erdős constant
- Champernowne constant, another example of a number obtained by concatenating a representation in a given base.
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