| 词条 | Smarandache–Wellin number |
| 释义 |
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: 2, 23, 235, 2357, 235711, 23571113, 2357111317, 235711131719, 23571113171923, 2357111317192329, ... {{OEIS|id=A019518}}. Smarandache–Wellin primeA Smarandache–Wellin number that is also prime is called a Smarandache–Wellin prime. The first three are 2, 23 and 2357 {{OEIS|id=A069151}}. 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 2, 3, 7, 719, 1033, 2297, 3037, 11927, ... {{OEIS|id=A046284}}. The indices of the Smarandache–Wellin primes in the sequence of Smarandache–Wellin numbers are: 1, 2, 4, 128, 174, 342, 435, 1429, ... {{OEIS|id=A046035}}. 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] See also
References1. ^{{cite book | last = Pomerance | first = Carl B. |author2=Crandall, Richard E. | authorlink = Carl Pomerance | title = Prime Numbers: a computational perspective | publisher = Springer | year = 2001 | pages = 78 Ex 1.86 | isbn = 0-387-25282-7 }} 2. ^Rivera, Carlos, Primes by Listing 3. ^{{MathWorld|title=Integer Sequence Primes|urlname=IntegerSequencePrimes}} Retrieved 2011-07-28.
External Links
2 : Base-dependent integer sequences|Prime numbers |
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