Primorial
For the 
th Prime 
,
The first few values for
, are 2, 6, 30, 210, 2310, 30030, 510510, ... (Sloane's A002110). 
is Prime for Primes 
, 5, 11, 41, 89, 317, 337, 991, 1873, 2053, 2377, 4093, 4297, ... (Sloane's A014563;Guy 1994), or 
for 
, 3, 5, 13, 24, 66, 68, 167, 287, 310, 352, 564, 590, .... 
is known to be Prime forthe Primes 
, 3, 5, 7, 11, 31, 379, 1019, 1021, 2657, 3229, 4547, 4787, 11549, ... (Sloane's A005234; Guy 1994, Mudge1997), or for 
, 2, 3, 4, 5, 11, 75, 171, 172, 384, 457, 616, 643, 1391, ... (Sloane's A014545). Both forms have been tested to
(Caldwell 1995). It is not known if there are an infinite number of Primes for which is Prime orComposite (Ribenboim 1989).
References
Borning, A. ``Some Results for Buhler, J. P.; Crandall, R. E.; and Penk, M. A. ``Primes of the form Caldwell, C. ``On The Primality of Dubner, H. ``Factorial and Primorial Primes.'' J. Rec. Math. 19, 197-203, 1987. Dubner, H. ``A New Primorial Prime.'' J. Rec. Math. 21, 276, 1989. Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 7-8, 1994. Leyland, P. ftp://sable.ox.ac.uk/pub/math/factors/primorial-.Z and ftp://sable.ox.ac.uk/pub/math/factors/primorial+.Z. Mudge, M. ``Not Numerology but Numeralogy!'' Personal Computer World, 279-280, 1997. Ribenboim, P. The Book of Prime Number Records, 2nd ed. New York: Springer-Verlag, p. 4, 1989. Sloane, N. J. A. Sequences A002110/M1691, A005234/M0669, A014545, and A014563 in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html. Temper, M. ``On the Primality of 
and 
.'' Math. Comput. 26, 567-570, 1972.
and 
.'' Math. Comput. 38, 639-643, 1982.
and 
.'' Math. Comput. 64, 889-890, 1995. and 
.'' Math. Comput. 34, 303-304, 1980.
- Paley's Theorem
- Palindrome Number
- Palindromic Number
- Palindromic Number Conjecture
- Pancake Cutting
- Pancake Theorem
- Pandiagonal Square
- Pandigital
- Panmagic Square
- Pantograph
- Papal Cross
- Pappus Chain
- Pappus-Guldinus Theorem
- Pappus's Centroid Theorem
- Pappus's Harmonic Theorem
- Pappus's Hexagon Theorem
- Pappus's Theorem
- Parabiaugmented Dodecahedron
- Parabiaugmented Hexagonal Prism
- Parabiaugmented Truncated Dodecahedron
- Parabidiminished Rhombicosidodecahedron
- Parabigyrate Rhombicosidodecahedron
- Parabola
- Parabola Caustic
- Parabola Evolute