Primorial prime
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In mathematics, primorial primes are prime numbers of the form pn# ± 1, where pn# is the primorial of pn.
pn# − 1 is prime for n = 2, 3, 5, 6, 13, 24, ... (Sloane A057704 (http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A057704))
pn# + 1 is prime for n = 1, 2, 3, 4, 5, 11, ... (Sloane A014545 (http://www.research.att.com/projects/OEIS?Anum=A014545))
The largest known primorial prime is 392113#+1, found in 2001 by Daniel Heuer (http://primes.utm.edu/bios/page.php?id=223).
The idea of primorial primes appears in Euclid's proof of the infinitude of the prime numbers.
See also
External links
- The Prime Pages - Top ten (http://primes.utm.edu/largest.html): keeps a list of the top ten primorial primes
- Coordinated Search for Primorial Primes (http://primorialprime.home.comcast.net/)
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