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A019546 Primes whose digits are primes. 87
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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]

REFERENCES

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.

LINKS

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

MATHEMATICA

Select[Prime[Range[700]], Complement[IntegerDigits[#], {2, 3, 5, 7}] == {} &] (* Alonso del Arte, Aug 27 2012 *)

PROG

(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, 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

CROSSREFS

Cf. A045336, A003631, A034844, A179336, A109066, A215927.

Sequence in context: A074491 A154385 A125525 * A104179 A096148 A211681

Adjacent sequences:  A019543 A019544 A019545 * A019547 A019548 A019549

KEYWORD

nonn,base

AUTHOR

R. Muller

EXTENSIONS

More terms from Cino Hilliard, Aug 06 2006

Thanks to Charles R Greathouse IV and Tony Noe for massive editing support.

STATUS

approved

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Last modified November 21 11:17 EST 2014. Contains 249777 sequences.