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Search: id:A005385
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| A005385 |
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Safe primes p: (p-1)/2 is also prime.
(Formerly M3761)
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+0
150
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| 5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459, 2579, 2819, 2879, 2903
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Then (p-1)/2 is called a Sophie Germain prime: see A005384.
Or, primes of the form 2p+1 where p is prime.
Primes p such that denominator(Bernoulli(p-1) + 1/p)=6. - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Feb 10 2004
Or, primes p such that p-1 is a semiprime. - Zak Seidov (zakseidov(AT)yahoo.com), Jul 01 2005
A156659(a(n)) = 1; A156875 gives numbers of safe primes <= n. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 18 2009]
Near subset of A161897. [From Reikku Kulon (reikku(AT)gmail.com), Jun 21 2009]
Contribution from Daniel Forgues (squid(AT)zensearch.com), Jul 31 2009: (Start)
A safe prime p is 7 or of the form 6k-1, k >= 1, i.e. p == 5 (mod 6).
A prime p of the form 6k+1, k >= 2, i.e. p = 1 (mod 6), cannot be a safe prime since (p-1)/2 is composite and divisible by 3. (End)
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Wikipedia, Safe prime
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MAPLE
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with(numtheory); [ seq(safeprime(i), i=1..3000) ]: convert(%, set); convert(%, list); sort(%);
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MATHEMATICA
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A005385=Select[Prime[Range[1000]], Plus@@Last/@FactorInteger[ #-1]==2&] (Seidov)
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PROGRAM
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(PARI) g(n) = forprime(x=2, n, y=x+x+1; if(isprime(y), print1(y", "))) (Cino Hilliard (hillcino368(AT)gmail.com), Sep 12 2004)
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CROSSREFS
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a(n) = 2 * A005384(n) + 1.
Cf. A007700, A023272, A023302, A023330, A057331, A005602.
Except for the initial term, this is identical to A079148.
Cf. A161897 [From Reikku Kulon (reikku(AT)gmail.com), Jun 21 2009]
Sequence in context: A151715 A090810 A092307 this_sequence A075705 A141305 A067289
Adjacent sequences: A005382 A005383 A005384 this_sequence A005386 A005387 A005388
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Feb 15 2001
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