Smarandache-Wellin number
Encyclopedia
In mathematics
, a Smarandache–Wellin number is an integer
that in a given base is the concatenation
of the first n prime number
s written in that base. Smarandache–Wellin numbers are named after Florentin Smarandache and Paul R. Wellin.
The first decimal
Smarandache–Wellin numbers are:
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. 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.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a Smarandache–Wellin number is an integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
that in a given base is the concatenation
Concatenation
In computer programming, string concatenation is the operation of joining two character strings end-to-end. For example, the strings "snow" and "ball" may be concatenated to give "snowball"...
of the first n prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
s written in that base. Smarandache–Wellin numbers are named after Florentin Smarandache and Paul R. Wellin.
The first decimal
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
Smarandache–Wellin numbers are:
- 2, 2323 (number)23 is the natural number following 22 and preceding 24.- In mathematics :Twenty-three is the ninth prime number, the smallest odd prime that is not a twin prime. Twenty-three is also the fifth factorial prime, the third Woodall prime...
, 235235 (number)235 is the integer after 234 and before 236.-In mathematics:It is the second number of the tenth row of a skewed Fibonacci-Pascal triangle ....
, 2357, 235711, ... .
Smarandache–Wellin primes
A Smarandache–Wellin number that is also prime is called a Smarandache–Wellin prime. The first three are 2, 23 and 2357 . The fourth has 355 digits and ends with the digits 719.The primes at the end of the concatenation in the Smarandache–Wellin primes are
- 2, 3, 7, 719, 1033, 2297, 3037, 11927?, ... .
The indices of the Smarandache–Wellin primes in the sequence of Smarandache–Wellin numbers are:
- 1, 2, 4, 128, 174, 342, 435, 1429?, ... .
The 1429th Smarandache–Wellin number is a probable prime
Probable prime
In number theory, a probable prime is an integer that satisfies a specific condition also satisfied by all prime numbers. Different types of probable primes have different specific conditions...
with 5719 digits ending in 11927, discovered by Eric W. Weisstein
Eric W. Weisstein
Eric W. Weisstein is an encyclopedist who created and maintains MathWorld and Eric Weisstein's World of Science . He currently works for Wolfram Research, Inc.-Education:...
in 1998. 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.