Euclid Number
The 
th Euclid number is defined by
where
is the 
th Prime. The first few 
are 3, 7, 31, 211, 2311, 30031, 510511, 9699691, 223092871, 6469693231,... (Sloane's A006862). The largest factor of are 3, 7, 31, 211, 2311, 509, 277, 27953, ... (Sloane's A002585). The of the first few Prime Euclid numbers are 1, 2, 3, 4, 5, 11, 75, 171, 172, 384, 457, 616, 643, ... (Sloane's A014545)up to a search limit of 700. It is not known if there are an Infinite number of Prime Euclid numbers (Guy 1994,Ribenboim 1996).See also Smarandache Sequences
References
Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, 1994. Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, 1996. Sloane, N. J. A. SequencesA014545,A006862/M2698, andA002585/M2697,in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995. Wagon, S. Mathematica in Action. New York: W. H. Freeman, pp. 35-37, 1991.
- Fiber Space
- Fibonacci Dual Theorem
- Fibonacci Hyperbolic Cosine
- Fibonacci Hyperbolic Cotangent
- Fibonacci Hyperbolic Sine
- Fibonacci Hyperbolic Tangent
- Fibonacci Identity
- Fibonacci Matrix
- Fibonacci n-Step Number
- Fibonacci Number
- Fibonacci Polynomial
- Fibonacci Pseudoprime
- Fibonacci Q-Matrix
- Fibonacci Sequence
- Fibration
- Field
- Field Axioms
- Field Extension
- Fields Medal
- Fifteen Theorem
- Figurate Number
- Figurate Number Triangle
- Figure Eight Knot
- Figure Eight Surface
- Figure-of-Eight Knot