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| In [[mathematics]], an '''integer sequence prime''' is a [[prime number]] found as a member of an [[integer sequence]]. For example, the 8th [[Delannoy number]], 265729, is prime. A challenge in empirical mathematics is to identify large prime values in rapidly growing sequences.
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| A common subclass of integer sequence primes are '''constant primes''', formed by taking a constant [[real number]] and considering prefixes of its [[decimal]] representation, omitting the decimal point. For example, the first 6 decimal digits of the constant ''[[π]]'', approximately 3.14159265, form the prime number 314159, which is therefore known as a '''pi-prime'''. Similarly, a constant prime based on ''[[e (mathematical constant)|e]]'' is called an '''e-prime'''.
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| Other examples of integer sequence primes include:
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| * [[Cullen prime]] – a prime that appears in the sequence of Cullen numbers <math>a_n=n2^n+1\, .</math>
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| * [[Factorial prime]] – a prime that appears in either of the sequences <math>a_n=n!-1</math> or <math>b_n=n!+1\, .</math>
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| * [[Fermat prime]] – a prime that appears in the sequence of Fermat numbers <math>a_n=2^{2^n}+1\, .</math>
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| * [[Fibonacci prime]] – a prime that appears in the sequence of [[Fibonacci number]]s.
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| * [[Lucas prime]] – a prime that appears in the [[Lucas number]]s.
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| * [[Mersenne prime]] – a prime that appears in the sequence of Mersenne numbers <math>a_n=2^n-1\, .</math>
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| * [[Primorial prime]] – a prime that appears in either of the sequences <math>a_n=n\#-1</math> or <math>b_n=n\#+1\, .</math>
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| * [[Pythagorean prime]] – a prime that appears in the sequence <math>a_n=4n+1\, .</math>
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| * [[Woodall prime]] – a prime that appears in the sequence of Woodall numbers <math>a_n=n2^n-1\, .</math>
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| The [[On-Line Encyclopedia of Integer Sequences]] includes many sequences corresponding to the prime subsequences of well-known sequences, for example [[OEIS:A001605|A001605]] for [[Fibonacci number]]s that are prime.
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| == References ==
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| * {{MathWorld | urlname=IntegerSequencePrimes | title=Integer Sequence Primes}}
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| * {{MathWorld | urlname=ConstantPrimes | title=Constant Primes}}
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| * {{MathWorld | urlname=Pi-Prime | title=Pi-Prime}}
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| * {{MathWorld | urlname=e-Prime | title=e-Prime}}
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| [[Category:Classes of prime numbers]]
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| {{Numtheory-stub}}
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I'm Edwina and I live in Eemnes.
I'm interested in Agriculture and Life Sciences, Conlanging and Swedish art. I like travelling and reading fantasy.
my weblog - help writing my paper