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Search: id:A056826
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| A056826 |
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Primes p such that (p^p + 1)/(p + 1) is a prime. |
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5
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OFFSET
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1,1
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COMMENT
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Note that (n^n+1)/(n+1) is prime only if n is prime, in which case it equals cyclotomic(2n,n), the 2n-th cyclotomic polynomial evaluated at x=n. This sequence is a subset of A088817. Are there only a finite number of these primes? - T. D. Noe (noe(AT)sspectra.com), Oct 20 2003
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 157, p. 51, Ellipses, Paris 2008.
R. K. Guy, Unsolved Problems in Theory of Numbers, 1994 A3.
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LINKS
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Eric Weisstein's World of Mathematics, Cyclotomic Polynomial
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MATHEMATICA
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Do[ If[ PrimeQ[ (Prime[ n ]^Prime[ n ] + 1)/(Prime[ n ] + 1) ], Print[ Prime[ n ] ] ], {n, 1, 213} ]
Do[p=Prime[n]; If[PrimeQ[(p^p+1)/(p+1)], Print[p]], {n, 100}] (from T. D. Noe)
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CROSSREFS
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Cf. A088790 ((n^n-1)/(n-1) is prime), A088817 (cyclotomic(2n, n) is prime).
Sequence in context: A084723 A107312 A083213 this_sequence A058910 A023394 A056130
Adjacent sequences: A056823 A056824 A056825 this_sequence A056827 A056828 A056829
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KEYWORD
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hard,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 29 2000
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EXTENSIONS
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Definition corrected by Alexander Adamchuk, Nov 12 2006
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