|
Search: id:A019434
|
|
|
| A019434 |
|
List of Fermat primes: primes of form 2^(2^k) + 1, for some k >= 0. |
|
+0
92
|
| |
|
|
OFFSET
|
1,1
|
|
|
REFERENCES
|
G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
R. K. Guy, Unsolved Problems in Number Theory, A3.
|
|
LINKS
|
C. Banderier, Pepin's Criterion For Fermat Numbers
C. K. Caldwell, The Prime Glossary, Fermat prime
Wilfrid Keller, Prime factors k.2^n + 1 of Fermat numbers F_m
Eric Weisstein's World of Mathematics, Link to a section of The World f Mathematics
Eric Weisstein's World of Mathematics, Fermat Number
Eric Weisstein's World of Mathematics, Fermat Prime
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics
Wikipedia, Fermat prime
|
|
MATHEMATICA
|
Table[2^(2^n)+1, {n, 0, 4}] (from Vladimir Orlovsky (4vladimir(AT) gmail.com), Apr 29 2008)
|
|
PROGRAM
|
(PARI) for(i=0, 99, isprime(2^2^i+1) & print1(2^2^i+1, ", ")) \\ - M. F. Hasler, Nov 21 2009
|
|
CROSSREFS
|
Cf. A000215, A159611.
Sequence in context: A023394 A056130 A078726 this_sequence A164307 A125045 A093179
Adjacent sequences: A019431 A019432 A019433 this_sequence A019435 A019436 A019437
|
|
KEYWORD
|
nonn,nice,new
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), David W. Wilson (davidwwilson(AT)comcast.net)
|
|
EXTENSIONS
|
It is conjectured that there are only 5 terms. Currently it has been shown that 2^(2^k) + 1 is composite for 5<=k<=32 (see Eric Weisstein's Fermat Primes link. - Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Sep 28 2008
|
|
|
Search completed in 0.003 seconds
|
