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A019546
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Primes whose digits are primes.
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85
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2, 3, 5, 7, 23, 37, 53, 73, 223, 227, 233, 257, 277, 337, 353, 373, 523, 557, 577, 727, 733, 757, 773, 2237, 2273, 2333, 2357, 2377, 2557, 2753, 2777, 3253, 3257, 3323, 3373, 3527, 3533, 3557, 3727, 3733, 5227, 5233, 5237, 5273, 5323, 5333, 5527, 5557
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OFFSET
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1,1
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COMMENTS
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Intersection of A046034 and A000040; A055642(a(n)) = A193238(a(n)). [Reinhard Zumkeller, Jul 19 2011]
Ribenboim mentioned in 2000 the following number as largest known term: 72323252323272325252 * (10^3120 - 1) / (10^20 - 1) + 1. It has 3120 digits, and was discovered by Harvey Dubner in 1992. Larger terms are 22557252272*R(15600)/R(10) and 2255737522*R(15600) where R(n) denotes the n-th repunit (see A002275): Both have 15600 digits and were found in 2002, also by Dubner (see Weisstein link). David Broadhurst reports 2003 an even longer number with 82000 digits: (10^40950+1) * (10^20055+1) * (10^10374 + 1) * (10^4955 + 1) * (10^2507 + 1) * (10^1261 + 1) * (3*R(1898) + 555531001*10^940 - R(958)) + 1, see link. [Reinhard Zumkeller, Jan 13 2012]
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REFERENCES
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H. Ibstedt, A Few Smarandache Integer Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, pp. 171-183.
Paulo Ribenboim, Prime Number Records (Chap 3), in 'My Numbers, My Friends', Springer-Verlag 2000 NY, page 76.
Sylvester Smith, "A Set of Conjectures on Smarandache Sequences", Bulletin of Pure and Applied Sciences, (Bombay, India), Vol. 15 E (No. 1), 1996, pp. 101-107.
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 1..10000
Chris K. Caldwell, The Prime Glossary: Prime-digit prime
Eric Weisstein's MathWorld Headline News, Two Gigantic Primes with Prime Digits Found
David Broadhurst: primeform, 82000-digit prime with all digits prime
Eric Weisstein's World of Mathematics, Smarandache Sequences
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MATHEMATICA
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Select[Prime[Range[700]], Complement[IntegerDigits[#], {2, 3, 5, 7}] == {} &] (* Alonso del Arte, Aug 27 2012 *)
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PROG
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(PARI) primedigits(n) = { local(ln, x, flag, j, y); forprime(x=2, n, ln=length(Str(x)); y=Vec(Str(x)); flag=0; for(j=1, ln, if(isprime(eval(y[j])), flag=1, flag=0; break) ); if(flag, print1(x", ") ) ) } - Cino Hilliard (hillcino368(AT)gmail.com), Aug 06 2006
(PARI) is_A019546(n)=isprime(n) & !setminus(Set(Vec(Str(n))), Vec("2357")) \\ - M. F. Hasler, Jan 13 2012
(Haskell)
a019546 n = a019546_list !! (n-1)
a019546_list = filter (all (`elem` "2357") . show )
([2, 3, 5] ++ (drop 2 a003631_list))
-- Or, much more efficient:
a019546_list = filter ((== 1) . a010051) $
[2, 3, 5, 7] ++ h ["3", "7"] where
h xs = (map read xs') ++ h xs' where
xs' = concat $ map (f xs) "2357"
f xs d = map (d :) xs
-- Reinhard Zumkeller, Jul 19 2011
(MAGMA) [p: p in PrimesUpTo(5600) | Set(Intseq(p)) subset [2, 3, 5, 7]]; // Bruno Berselli, Jan 13 2012
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CROSSREFS
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Cf. A045336, A003631, A034844, A179336, A109066, A215927.
Sequence in context: A074491 A154385 A125525 * A104179 A096148 A211681
Adjacent sequences: A019543 A019544 A019545 * A019547 A019548 A019549
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KEYWORD
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nonn,base
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AUTHOR
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R. Muller
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EXTENSIONS
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More terms from Cino Hilliard (hillcino368(AT)gmail.com), Aug 06 2006
Thanks to Charles Greathouse and Tony Noe for massive editing support.
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STATUS
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approved
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