### Integer-sequence prime

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.

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 is called an e-prime.

Other examples of integer sequence primes include:

• Cullen prime – a prime that appears in the sequence of Cullen numbers $a_n=n2^n+1\, .$
• Factorial prime – a prime that appears in either of the sequences $a_n=n!-1$ or $b_n=n!+1\, .$
• Fermat prime – a prime that appears in the sequence of Fermat numbers $a_n=2^\left\{2^n\right\}+1\, .$
• Fibonacci prime – a prime that appears in the sequence of Fibonacci numbers.
• Lucas prime – a prime that appears in the Lucas numbers.
• Mersenne prime – a prime that appears in the sequence of Mersenne numbers $a_n=2^n-1\, .$
• Primorial prime – a prime that appears in either of the sequences $a_n=n\#-1$ or $b_n=n\#+1\, .$
• Pythagorean prime – a prime that appears in the sequence $a_n=4n+1\, .$
• Woodall prime – a prime that appears in the sequence of Woodall numbers $a_n=n2^n-1\, .$

The Fibonacci numbers that are prime.

## References

• MathWorld.
• MathWorld.
• MathWorld.
• MathWorld.

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.

Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.